Do you have any thoughts or theories about what Thjazi's paint ritual will actually do? Though we don't have the most knowledge about its effects, we do know the ingredients and the intentions they've been given.
I'm personally inclined towards enlisting some or all of the orc souls that were captured in Gavzidra. Both the theming of KoTher'ai and the ringing of the pariah blades call orcs to war, and it seems like Thjazi was aware of the Tachonis' undead army. Additionally, the way Tsul'rekshi described the way the orcish souls would need to be taken care of after being freed reminded me of the reasons the seekers formed the magpies.
The afterlife that Azgra intended for the Rungjani was no reward. The Dying Fields of Zgratu'uluk was not a paradise promised to the orcs for their service in piously dying as foot soldiers enacting the endless slaughters of his perpetual war. The Rungjani had in death what they had in life (3: The Snipping of Shears): blood, suffering, and presumably war.
With the death of Azgra, these Fields are gone, as it is with all of the afterlives in the halls of the Shapers (2: Broken Wing). Still, the River Gavzidra that bore orcish souls to them still flowed, and the Order of Azgra binding those souls to the river still lingered as a curse. It is this jailer's cell of a curse that Tsul'rekshi overturns, destroying the last of Azgra's decrees on the Rungjani and liberating the souls of the orcish dead (27: Complicated Questions).
Would enlisting those souls to go to war not be returning them to that freshly-broken jailer's cell? How would having them march in death as they did in life to fight against the legacy of Tansul in Obridimia differ from the Order of Azgra, merely taken for one's own ends under a change of commander? Is it not the same as House Tachonis and their scar that binds souls into service after death? Are the Rungjani to be always soldiers?
The Falconer's Rebellion was fought "when they realized that a world that had risen up against the tyranny of the gods had, in the span of a few short generations, replaced that tyranny with ones of their own devising" (2: Broken Wing). Thjazi was a soldier and asked much of his compatriots, but I do not know he would devise a new war for the Rungjani dead.
I do not personally feel that the components call to war specifically.
The letter from the Professor to Thjazi references plowshares. Thimble remembers that it is as in the idiom swords to plowshares but applied specifically to magic and arcane objects. Any Shaper-era spell or object is only going to "shape the world into the shape that the Shapers wanted it," thus to commit sacrilege and profane an object to change or alter it away from its original purpose is important—swords to plowshares (26: Council of Heroes). Thjazi and the Cloak as individuals were not employing objects from the time of the Shapers in their original meaning and purpose. With that context then, the original use of the Pariah Blades as swords is not of interest to the Cloak in the context of their goals, for example.
The ringing of the Pariah Blades are not calling the orcs to war. The sound they make as Shadia uses them for busking fills the Rungjani who hear it now with "a sense of pride and vigor and joy of life" (23: Buried Truths), and Brennan attributes the company "having fun with it, making exciting choices, rediscovering stuff in the moment" during an immensely successful rehearsal to "something about the ring of those Pariah Blades" (24: Good Tidings). The sound inspires a joie de vivre, an exultation and exhilaration for life, and it fosters a creative spirit. The Pariah Blades were originally forged to liberate the Rungjani through waging war against the god of war, but we must not focus on that now. They already served that purpose and were reforged toward a new one, thus their prior purpose of "war" is not of interest here. Thaisha says it herself, when she goes to do this reforging, "They had their task. They killed Azgra, they freed our people, and now they are props for a story that we will tell so that our people will always know the story of what we've overcome." She finds there is nothing for her to reforge because Shadia has already done so by using them as theatre props, rather than tools of war (28: Chasing Shadows). They are no longer weapons—they're storytelling devices.
It is similar with the paint rendered from Gavzidra, the blood of the orcish people condemned to flow as this river so they carry Azgra's first injury as their own in perpetuity. As above, Gavzidra's purpose was to bind to the souls of the Rungjani and ferry them to the Dying Fields. The Dying Fields are absent, so it binds these souls. It feels significant that they took the river to Tsul'rekshi specifically. She potentially implies that any sufficiently powerful demon could have remade it ("seeking a demon"). However, Tsul'rekshi, as a paint maker, remade the blood into, out of all possibilities, paint. Murray, when she tastes it, says: "It is no longer blood, but it's like they rendered the paints from blood to create, to create stories, to create dreams, to create figments, to create things that are not real" (24: Good Tidings). These resulting paints were gifted to Hal by Thjazi ("with all my love", 2: Broken Wing), implicitly for his theater, and used by Shadia to paint a narrative of Rungjani history on its walls. Gavzidra is now a medium for storytelling.
Both the Pariah Blades and Gavzidra are elements now of Hal's play, KoTher'ai. It is a play about a revolutionary, but it is not a story about war itself. It is about the will and desire and dream for the freedom of the Rungjani from Azgra, one that did not begin with the Shapers' War but existed long before it. It is, as Thaisha says, a story about what the Rungjani have overcome (28: Chasing Shadows). It is a story about the rejection of the will of Azgra and of a defiance against that carried by Vokjan Murzat. KoTher'ai is about the Rungjani becoming something other than merely the tools shaped by Azgra for his purposes and their striving toward an order and meaning other than that which they gave him.
However, I feel that the play is not the spell component. The component is the amphitheater itself, and KoTher'ai is the means by which it is converted to a plowshare. Hal is in the place of Tsul'rekshi. By staging this play, he reshapes the Dithyramb of Azgra into the Hallowed Round, from a place to appease the god of war with song and dance into a place where the Rungjani tell stories.
Blade, blood, theater—all repurposed toward Rungjani storytelling.
The components of this spell or ritual that Thjazi and the Cloak are preparing at the Hallowed Round being the Pariah Blades (a weapon that slew a Shaper), Gavzidra (a means to the afterlife), and the Hallowed Round (a temple to a Shaper) generally fits the components that made up the coffin of Olbalad: Termina (weapon), Olbalad (psychopomp), and the plates (temple). Now, I admit that there's elements that are strange, such as wood from the Mournvale on the coffin and no clear sense of what the purpose of the Stone of Nightsong has here or whether it was intended for the work happening at the theater, but I have no good answers for that at this time.
None of this as of yet gets to what Thjazi and the Cloak were actually trying to accomplish with the spell cast using these components. Admittedly, despite "components" there being word 1,200 of my answer: I don't really have any concrete ideas. Yes, I know, this is a very long way to say "I have no idea."
That said, I can say that I believe that Thjazi and the Cloak were not merely attempting to do what House Tachonis was doing. While the Cloak moved against House Tachonis, it does not necessarily follow their modus operandi to employ the same methods. They tracked the movements of House Tachonis and the Sundered Houses closely, but toward the purpose of maximizing their own limited resources by allowing the Sundered Houses to first identify sites and objects of power, then taking them to make plowshares (27: Complicated Questions). From that, I am reluctant to assume that the goal is to create their own counter-army of the dead.
What then were Thjazi, Mara, and the Cloak doing with these pieces? We do know something beyond the components themselves because we have a letter hinting at their goals (26: Council of Heroes):
If all has gone well, you have the stone in hand. We'll need the steel. And you said you can convince her to reshape it into an anchor. If not, anyone in the family can make plowshares. Once it's done, the next step is to bring it to the field. Our wings are leading a charge against the border to draw the locals away from the site.
That hot shot I mentioned will meet you there and help prepare the arch from steel to stone. Please try to temper his confidence with pragmatism. Yes, I know you are precisely the wrong person for that.
Still remember, until a stable trinity of bridges are built, it is vital that the blood be protected. I trust that you have disguised it well. With any luck, the next time I see your face, we will have undone the damage of our first attempt. More than one door will be open to us from there.
Until then, I search for suitable anchors for the remaining four. We may need more hands soon after.
The "trinity of bridges" is of interest here, as before I noted that both the elements for what is set at the Hallowed Round is, generally, a trio of like items as is the components of the coffin. Three items associated with Azgra, three items associated with Rauwyn, one of each from the same trio of categories. The Stone of Nightsong similarly fits into one of these categories. That said, entirely likely that the trios aren't the trinity of bridges. Bogrey ("hot shot") is supposed to be meeting Thjazi at a place after Mara ("wings") goes into the Tenebral Reaches ("across the border") to draw presumably House Tachonis ("the locals") away from it, so that Bogrey can prepare "the arch" from the Pariah Blades ("steel") to the Stone of Nightsong ("stone"). Bogrey and Thjazi are supposed to be working on bridging the set including the Pariah Blades to the set including the Stone of Nightsong, perhaps?
Now, rounding back, there is the matter of the souls of the late Rungjani liberated from the paint. They do, as you've pointed out, need somewhere to go. These plans ultimately all work against House Tachonis, who have dominion over death. House Tachonis wishes to destroy the Old Path, and they employ this scar to compel people into their servitude in death (18: Vindicta & Vale). It stands to reason that, because House Tachonis gains power with every death and every soul in the Tenebral Reaches (3: The Snipping of Shears), they seek to prevent souls from leaving the Reaches into alternate afterlives, including the Path and any other means that might be found.
However, to truly free the peoples of Pasitar from the order of the Shapers, one needs also to free them from the afterlives that they expect or might even be bound to. The Path, in place since before the Shapers, guides the spirit back into the world to new life, but you cannot make everyone walk it. Though the Shapers are dead, their hold remains on the world in the truth of the problem of the afterlives. It has been often said by many in the fandom, but perhaps Thjazi and the Cloak sought to continue the work of the Shapers' War and continue to destroy that hold of the Shapers by giving to all in death what they have now in life: a freedom and liberation from the Shapers by facilitating their means to cycle back into the world, as their spirit did in ages of yore. This, in turn, goes against the plans of House Tachonis.
To do so, one needs to extend this liberation to those souls already passed into the halls of the Shapers. Brennan remarks that one of the big philosophical questions of post-Shaper Aramán is what happened to those vanished halls and the souls within them. The current leading research is that these afterlives still exist but became untethered without the gods (2: Broken Wing).
If one's goal is to liberate the souls of the dead from the order of the Shapers by also unmaking the rules of death they created, one needs to then tether those halls back into the cosmology—build bridges back to them. At that point, this becomes a structural engineering problem, and any stable bridge needs anchor points. The Professor is working on a "remaining four", and if we surmise that the orcish set is complete, the halfling set with the coffin is complete or in progress, and the elvish set has its pieces identified and in progress, this totals seven. Perhaps each these trios of items, turned to the opposition of the order of the Shapers and the necessities birthed by their structuring of the world, are serving together as those anchor points between each afterlife for these trinity of bridges to ensure that the bridges do not collapse and swing their point of egress into, say, Faerie.
"The damage of our first attempt" is precisely that. Their first attempt was not anchored (26: Council of Heroes), and it caused the dead and necromantic energy to spill into Faerie, causing the doors to be closed to prevent the death of the realm (3: The Snipping of Shears). By accident, the Cloak pointed the dead at Faerie, rather than wherever they wanted these bridges to go.
The paint is at the exact midpoint where necromancy and conjuration meet, where conjuration is "the deeper, more profound note" (20: The Vanishing). Necromancy, we can surmise, comes from the paint's relationship to the afterlife as something rendered from the River Gavzidra (27: Complicated Questions). It is what positions this reshaped paint into a photo negative of the Stone of Nightsong, which held a similar purpose in the time of the Shapers (24: Good Tidings). As a result, the conjuration is the more fascinating and mysterious element. Conjuration is a magic of creating things and of moving things from one place to another. It is the school of manifesting out of nothing, of summoning, of teleportation, of doors.
The Professor hoped that when he next saw Thjazi they would have undone the damage they had caused Faerie, and from there, more doors would be open to them. I am not the first to suggest this, but perhaps in the course of events at the theater, the intent is also to re-open the door to Faerie, to the realm of abundance and of life, an opposition to the Reaches and the power of House Tachonis. The power of the fae forms an important relationship with demonic and primoridal magic, after all (27: Complicated Questions). Another trio.
For the ultimate goals, perhaps, Thjazi and the Cloak had intended at the Hallowed Round to finish creating an anchor for the Rungjani living and dead that would show them a path fully and finally beyond Azgra by bending their implements of war into mediums for storytelling, and with that begin to offer a route back into new life for those in the Dying Fields and in the Reaches, the first of many new paths, out of the dominion of the Shapers and House Tachonis alike. The woods are deep, as Thaisha says, that's why we cut a Path (28: Chasing Shadows).
That's my best guess. Connect seven points with three lines.
