Reading your ideas has made me realise just how out of touch I am with most modern games XD
I think Mortal Kombat dating sim definitely has legs. Maybe you could have combo moves that result in compliments, empathy, hugs etc. and... if it goes badly, the pair just start fighting each other!
Our last game was actually a visual novel with lots of violence. Couldn't find a way to throw in any action scenes, sadly. A VN that turns into a FPS halfway through for no apparent reason would be cool...