I don't know if it will take that much time, if she sees what he is doing for the girls.
He's doing his best with Chika.
Inspired Futaba to stand for herself and go to the gym.
Helped Sana to comunicate.
He did try his best to help her find a job.
Is helping Touka get more grounded instead of her usual pedestal.
If she sees that he is doing his best she may grow to think the better of him sooner than expected.
It might be harder than that though. Yumi’s armored with the concept of “why the fuck do all you guys like your teacher this much it’s creepy!”, so she likely won’t believe any good progression from others because of all the girls’ unusually high affinity towards him. Not to mention the fact that hidden within most good progression of others is Sensei's ulterior motive, which is also something Yumi constantly points out. This altogether makes progressing with her difficult.
Sensei also had some good progression with her regardless, and she felt that as well. However, this apparently only brings you to as far as an
extremely sweet note as Christmas gift, and not what’s beyond. She needs A LOT more pushes to nail the coffin and finally hook up to Sensei.
Aside from what ppl have talked about, one option is that Yumi can
convince herself that she only deserves to be with a scum of the earth like him. Hooking up with him also potentially keeps this asshole at bay and serves as a "damage control" for others girls (imagine this is what she conjures as a solution to stop Chika from
dating Sensei). This will be to a point that Yumi essentially lying to herself in seek of justification.
The other option is to really improve their relationship by solving their issue from the very beginning: that traumatizing kiss, the major sources of her distrust, and her distrust for others when she heard "he isn't that bad".
Since she is already aware of his episodes (but I forgot if Yumi ever made the connection between that kiss and his blackout), I guess it can work the other way around by letting Yumi have a blackout and having Sensei snap her out, so she can finally understand that he is not
as bad.
Final option is to just let her survive a reset (somehow); surely surviving an apocalypse accelerates that process right? (saying this only because topics like these was our current and only success to have Yumi really consider sleeping with him)