"I suspect the University group was convinced to do this by the Ishinomaki Group,"
While the initial thought is that this seems to be a lie, it might not be. The University group has been planning this for at least a year, but even at that point they were nervous about the whole thing. From Mami's impressions, I'd guess that they don't have the strength/motivation to properly stand up to the Sendai group on their own, but if someone was backing them up they'd be more amenable.
At the same time, both groups know that they can't deal with Sendai as a whole, which is why they had to bide their time for an opportunity when the group was split.
With only 4 in the University group, they probably needed to wait until Akiko was out of the territory to feel they had a decent chance. 4 vs 2 on the Sendai front, ?? vs 3 on the Ishinomaki front.
Actually, wait. Need to calculate, since I can't find any explicit numbers for Ishinomaki.
There are 22 total girls in this fight. We know Sendai has 5, and University has 4, which means 13 between the other two. If Fukushima has 6, that leaves 7 in Ishinomaki, which makes a bit more sense.
So the Ishinomaki front was 4 vs 2 for Rin/Sakura, and 3 vs 1 for Akiko.
In any case, balancing the numbers clearly needs Akiko in Ishinomaki for the group effort to have a chance. If Akiko was still in Sendai, the University group wouldn't be able to take them on. Thus, our pulling Akiko out of Sendai advanced the timeline. Oriko was vague about when it 'originally' happened, and even advancing it one day would count, technically.