Maybe it's just me hallucinating logic into canon writing, but after Trespasser and Tevinter Nights, I had a distinct impression that the Antaam presence is a huge cover-up for another operation carried out by the Ben-Hassrath on several fronts, including Rasaan searching for Fen'Harel's "true name" and other forces hunting for ancient elvhen magic.
In Three Trees to Midnight, the Antaam leader Bas-taar was eventually taken out by a BH agent disguised in his own ranks. Which had me thinking, wherever the "splinter Antaam" went, they would have had BH agents sitting on the leaders' tails to watch them, report back and... something more. Which got me thinking further: what if this was the way in which Stenrishok kicked a bunch of dissenters and otherwise troublesome individuals out of Par Vollen, to let them wreak havoc in the South, but not counting on them to accomplish too much? And if any of these lords managed to get too far before the mainland forces got rid of them, or before the splinter Antaam itself divided and dispersed completely, the undercover BH agents were there specifically to clean up the mess.
In the meantime, the real operation and the real concern lied with Solas, his network, and ancient magic, as if the interests were clashing in a way more specific than the everlasting yet seemingly lukewarm cultural conflict. It's already alarming that the Qunari have issued a sudden takeover exactly when Fen'Harel was activating his agents worldwide, as if to dispose of the needle moving in a haystack by turning the entire barn upside down. Everything between Trespasser, the parts of Tevinter Nights meant to follow right after, and the comic book arc from Knight Errant to Dark Fortress smells of mess, rush and panic around the Qunari trying to get to Fen'Harel before everyone else, preferrably without having to tell any outsiders about what's to come. Even as useless as The Missing generally is, it shows that every location in Tevinter where Varric and Harding are searching for Solas, the Antaam is already there, but seemingly with poor results (because the people doing the real work might be staying invisible). Meanwhile, the Ben-Hassrath manages to dodge some extra threats, like the personas appearing at The Teahouse (which makes me think again: The Ben-Hassrath might have skipped the meeting because they expected an Executor, Solas's agents, or both. Either that or "The Bard's Tale" from The Dread Wolf Take You didn't lie in this regard, and Solas actually managed to catch them and the Siccari agents in a trap beforehand).
Trespasser highlights that the real threat to the Qunari interest is not of mainland Thedas, does not represent mainland Thedas in any way that matters, and is brewing a major act of destruction against the mainland Thedas' status quo by themself, therefore changing the official geopolitical situation in mainland Thedas (through The Dragon Breath or else) would do nothing to inconvenience The Dread Wolf in the long run, even if it has other advantages.
It would have been so much more juicy if both Daathrata The Butcher and Dragon King were constantly facing a threat from Par Vollen, but couldn't admit it. Even The Iron Bull gets a ceremonial assassination attempt as a goodbye if the Inquisitor prompts him to save the Chargers. It makes sense for these rogue leaders to abandon the ideology and keep wanting to conquer and rule in their own name and because of their own pride. I don't mind the idea that being sent off on an operation by themselves went in their heads - after all, the Antaam forces being torn away from their "heart" and their "brains" is not a healthy state based on the existing lore. Especially if they were already dissenting or too brutish for Arishok's taste.
But what if these leaders' "occupation" over their respective places in Thedas was basically a theatre play, mostly possible due to some... concessions made to the local populace. In exchange for espionage that would hopefully protect their hides from the prowling Ben-Hassrath. Make Ivenci the Grima on his shoulder who says "Yes, Daathrata, you are so smart and open-minded, let's get you a massive portrait from the local genius", then works with House De Riva. The narrative could have used both Antivan Crows and The Lords of Luck as factions in the know -- who Fen'Harel's agents are, who the Ben-Hassrath are, and how to detract both groups away from the entire mess. But obviously, they would juggle that information carefully, and for a high price... Both The Crows and The Lords of Luck are ideologically neutral, with a potential for betrayal and infighting. Daathrata, at least, was outlined as showing awe and appreciation for Antivan culture. Almost as if he only understood learning through the lens of conquest, and in my mind he would have relished the frail illusion of power if he were allowed to satiate his real guiding impulse: curiosity.
And with the hints of lore about the Devouring Storm, what if BH were collecting ancient magical artifacts (per Half Up Front) to carry out a controlled detonation of sorts, because the artifacts had better be destroyed than consumed by the Enemy?