Schemers (Team Dol-Rungja aka Team Traveling Circus)
I've already explained in this post why I think they will not have enough people for a schemers team in Dol-Makjar.
Halandil has to relocate his troupe now that they have defied House Halovar. Brennan once described Dol-Rungja as "the capital city." It might have less Sundered Houses influence since Kahad was at least originally a land of mostly orcs and that should make it a safer place for his troupe. Also bonus, he will finally get to hang out with Thaisha.
Thaisha has to meet with her great-grandma, Scyvah. She already kind of committed to doing it after her business is done in Dol-Makjar. She might like to go to the Hall of Mercy to save the Old Path but it seems like Hannan might go and he could ensure her that he represents her interests. Also, since Shadia was part of the play she is in as much danger as the rest of the troupe and she will likely want to keep her safe.
Wicander wants to find Armas. He isn't going to do that in the ocean or in other planes. He also want to undermine the Creed and he can't really do that in the other team with the exception of the time the Soldiers will pass through Timmony. Also bonus, he gets to hang out with his former Teacher Halandil.
Tyranny wants to undermine the Creed too. Also, I don't see her seperating from Wicander some time soon. It will probably happen eventually when there are strong and clear reason to seperate them but none are present currently. Her sole mission right now seems to be to protect Wicander and also to turn him awsy from the Creed which also goes into undermining the Creed. Tyranny will want to make sure Wicander dosen't believe things that are solely based on Candescent Creed teachings.
Mara might want to join the Schemers to thank Halandil for completing the ritual by helping him protect his troupe. It also helps that Halandil is the brother of Thjazi and she might want to get to know Halandil for that reason.
Seekers (Team Golden Orchard to Faerie aka Teor and his Niblings)
Thimble has stated multiple times that she wants to go to the Golden Orchard. Also it looks like ritual will reopen the doors to Faerie. That is relevant here because Thimble would feel it like she did when they closed and it is reasonable to assume if not downright know that there is a door to Faerie in the Golden Orchard. Thimble would want to make allies with the fey considering what House Tachonis did to the Golden Orchard. Also, Temelow said that fey were disappearing in Dol-Makjar. Thimble could evacuate the Dol-Makjarian fey there since she is looked up to by a lot of fey. I also don't think she would leave Occtis so soon after learning that he died when she wasn't there. She is going to be protective for a little while.
Julien said he would go to the Golden Orchard with Thimble. It looks like he wants to see Alba. Also, Julien being a vassal knight of House Royce, he would have a lot influence with the fey. Bonus that Occtis is there because he still has an obligation from his father to protect Occtis.
Occtis would probably have some things to say about Alba's curse if he examined her. Occtis adds the lord factor with any diplomatic interactions with the fey royalty (yes they were described as princes and princesses). Bonus, he gets to hang out with his buddy Thimble.
Azune's reasons for going are pretty much exactly the same as Occtis'. He might have things to say about Alba's curse and Thimble is a plus. Also, it dosen't rule out Team Traveling Circus but going to the Golden Orchard would be less stressful to him than the Hall of Mercy. At least that is what the perception would be but he desperately needs to avoid stress with how many breakdowns he has had. Azune is probably the most strategic thinker of the pcs and he would want to make sure it goes smoothly with the fey considering how much of a big ally they could be.
Teor said he would go. Also, it looks like he has something to do with the fey judging by that one cold open when his amulet was feeding into fey magic for no apparent reason.
Soldiers (Team Timmon's Rock to the Hall of Mercy aka Team Oh Gods Oh No Oh Fuck)
Vaelus said that she wanted to go home. The Sea Door isn't home for her but I think it is awfully close. She could probably send a bird to meet her if there is anyone she wants to talk to. It also helps that she probably has insight about the Wastes and that helps because it seems like it partly covers the Sea and it seems the Sea Door is in that area. Since she has likely been on a ship before to travel she probably has the most sailing experience than all of them possibly with the exception of Thimble because she had to go overseas to steal the Stone of Nightsong. Also...
Light must they wield to keep at bay the Guardians of the Veil and bear their lord forth unto the Sea of Lachris, where the blood of old may give new life to rotted flesh and summoning forth the power of the living upon the dead. But lo and be forewarned! Should the mist know but a single mortal breath, the spell is broken, the lord consumed by Death itself.
Vaelus being a paladin and a person with immortal breath should help. I also think that they might get an army of celestials from the ritual. The army would be going to the Sea of Lachris with them. Vaelus could lead them considering that they might be grateful for her part in the ritual and because she might be the expert on celestials since she is a priest of Sylandri who could have seen celestials before being is so old. It also helps that she was in that meeting with Gus because they have an invite to stop by his capital on their way to Houndsport. This team could ask for a ship from him.
Bolaire isn't mortal either. He also may not need to breethe. If he can starve his host of food and possess a host that practically disintegrates after he releases them I imagine he can starve his host of air without any consequences. Also, Bolaire was in the team saved Gus so that adds him some points for when they meet him again.
Kattigan was in the same team that rescued that petrified hound so that is good for a King Gus meeting. He also just learned that Primus is responsible for the disappearance of his wife and child so getting to thwart a Tachonis plan should be good for him. He will also probably get a chance to fight some Tachonis lords and ladies because Doset and Univere were heading to Houndsport and Petra's and Ryah's letter said that they along with Segundus are supposed to go to the Sea Door. It seems like Koral will be delivering the gem she stole from the Golden Orchard to at least to Houndsport. A great opportunity for revenge, questioning or leverage to get his family back. Also, House Tachonis threatens the Old Path and he likely gets his power from it in their plot with the Hall of Mercy. Kattigan would also be their guide since he has just been in Timmony.
Murray had a vision realting to the Sea of Lachris. That might give her a sense that she feels like she is supposed to go there. She can also identify and talk to that gem with the book if she finds it. She was also part of the saved Gus and he is very thankful for that.
Hannan said he would go with Vaelus to the Mournvale. They may not dock but the Sea Door is still pretty close. Hannan could also join to use that seed since only fey, hounds of the King, and followers of the Old Path can use it. He can also represent the Old Path's interests more strongly than Kattigan. He is also immortal.