For a proper argument, there are moments where you can quite catch when each gitl has legitimate attraction with the character. Shizune, for one, starts having small crushes on Hisao during the end of ACT I festival, when she goes around showing the stars and accidentally get a little close to Hisao.
She approached him first more as an obligation as the class representative, student council president, and fenerally get-shit-done taskmaster, but it develops more than that at the end of ACT I and further into ACT II where genuine interest starts to show.
Hanako's starts around ACT II; ACT I's finale with 'checkmate' is more of her getting comfortable around him--just like how she feels around Lilly. She has that growing crush on Hisao after ACT I, specifically during their outing together, I believe (when you first saw her with her casual clothes).
Rin's is more of 'your guess is as good of mine'-kinda, but it is for sure before or after her psychadelic trip with codeine (was it codeine? I keep on thinking weed and her suddenly singing 'smoke weed everyday')
Emi seems to have an interest on Hisao after he joins her every morning for runs since they go out fairly quickly.
Lilly is what actually confuses me the most, so i'm not going to bother.
Of course an easier explanation would be 'Hisao is the master of romance and all that medicine he consumes unleashes massive pheromones that even attracts Kenji and challenges Jigoro.'
Now on to self-insert OC.
If you've read my stories, you'll notice I have my own self-insert since he has carries the same name in different 'dimensions'--although mostly, he is acting more as a supporting cast and background character. The KS girls are reserved for Hisao and Hisao only!
The thing about self-inserts is how dangerous they can be--especially if they come from say...another country or something (e.g US/UK/RUS/etc.) and transfers to Yamaku, somehow understanding the language and culture perfectly, and gets to woo the girl they want. It is a way to 'live' off fantasy understandably, but at the same it is breaking the limit of 'suspension of disbelief' and can ir may be considered as a Mary/Marty Stu--the worst kinds of character (second to NTR-ers in my book).
Just be really-really cautious when you put your self insert. It's a risky business when writing fiction (not just fanfiction), and you especially don't want your character to end up like that girl from Twilight.