@ Senpai - Made an edit. Anyway, maybe have her treat Dan like he's not worth her time.....only for Ichika to yell at her due to her spoiled attitude.
Also, none of the other heroines (Bar Rin) really show signs of sexism. Even Laura the proud soldier girl didn't have any.
The IS being hyped is possible, actually. I use this in both FI and Shadow as plot point's
Going home, be back in an hour.