Rin probably still going there because she's already cadet rep before Ichika is made a pilot, just less eager than canon.
Charlotte would be there too, just not in drag, doing teen-spy thing just because.
I think one teacher for one student is too unfair for the rest, more like one teacher for one group with commonality, and that's more or less unofficial assignment (like a teacher-assisted study group). Of course, this assuming things don't play like canon while the rest... well, they just didn't care about fighting, so the group is small enough as it is.
And if you insist putting the OC in, no one stopping you
