But what if Sendai isn't? Much of your plan immediately collapses.
A legitimate objection.
Consider that at present the situation is Sendai + Fukushima vs Ishinomaki + the University group. This totals 22 girls.
Full collective will be Sendai + Fukushima + Onagawa + Tokyo vs Ishinomaki + University + Osaki + Tome. Probably doubles the total number.
Home team is Ishinomaki; all others are pulled in from elsewhere.
University group is also from Sendai; a splinter group, since Akiko's team is considered the 'main' group.
We might also want to consider the implications of Sakura being used to teleport Akiko in during the Masami affair. Akiko and the other two remaining behind in Sendai as defensive elements? Or it's not really safe for them to travel on foot? Of course, maybe they just don't want to be bothered with such lesser forms of travel.
In any case, the University group followed Sendai to Ishinomaki, and teamed up to take Sendai out while they were outside their home territory. Since Sendai and Ishinomaki are on opposite sides of Mitakihara, the territory grab is clearly the University group's (taking over all of Sendai once the competition is gone), while Ishinomaki doesn't get any new territory out of this. Ishinomaki must be getting something else out of this conflict.
Given that Sendai was there on a healing run, either Ishinomaki doesn't care about losing the healer, or they may be expecting to take Rin as plunder — their own healer, since she'll be pretty helpless once the rest of her team is gone.
Sendai was present for their healing circuit, which means they didn't view Ishinomaki as intrinsically hostile. University group is already present, as the Fukushima group is being pulled in to aid Sakura and Rin, who were pinned down by the University group. Fukushima is thus panic support, and the basic attack originates from Ishinomaki + University.
Now, how could Sabrina's interference in the Masami incident have sped up the conflict? The most obvious change is that Sakura went and fetched Akiko after Sabrina's first run-in with the pair. That takes Akiko out of Sendai. Did the University group take that opportunity to slip out from under the Sendai group's watch, to be waiting for them in Ishinomaki?
So, both of those groups have some grudge against Sendai (not hard to fathom). University wants territory; Ishinomaki (probably) wants the healer; I can't imagine a grief seed payment of less than ridiculous size being enough on its own to get them involved in a war (though it might just be a long-standing hate grudge).
In that case, how will they react to the scenarios?
1) Sendai teleports out on their own. Fukushima should be in a safe, defensible position. Other groups haven't arrived yet. Once other groups arrive, the conflict re-starts.
2) Sendai extraction. Fukushima left in the lurch by their ally suddenly disappearing. Probably put in bad straights. No trace of where Sendai went if we use Time Stop. If Fukushima is vulnerable, University will likely to stay to finish them off, or at least hurt them. Otherwise, if they can't trace Sendai, they may return to the city and simply post claim by virtue of Sendai not being there to contest it, possibly looting Sendai's HQ. Sendai is then in the difficult position of trying to fight their way back into their own home.
If we were responsible for the extraction, there may be the expected obligation for us to help out either Fukushima or getting back into Sendai. If Sendai made their own way out, Fukushima is probably in a defensible position, and waiting reinforcements from allies. Once allies show up, the fighting starts up again.
3) If the University group wants the removal of competition, and Ishinomaki wants their own healer, our stepping in just paints a big red target on our back. On the other hand, with us being able to facilitate near-free healing services, Ishinomaki may back off on the healer. And with us being able to cleanse grief seeds, Sendai doesn't actually need the Sendai territory, and can cede it to the University group. That still feels like a less than ideal outcome, but I'm not sure how to improve on it offhand.
However, by removing the toy everyone was fighting over from play, that pretty much short-circuits the rest of the conflict, as long as we can get it done before any of the other groups arrive. Making sure Fukushima gets out may also be important.
Looking at all the details, I still feel that Sendai is the lynchpin in this war, but the means of resolving it is a bit more subtle and difficult to work through. The arrest deception may not be sufficient.