It should work that when the girls get into bed to go to sleep and the screen fades to black, that before resuming the cut scene you could potentially add some sort of popup asking would you like to save, without giving full menu access? Which is something I’ve seen you offer in some other cutscenes? I think? (That’s roughly the halfway point).
Although if this is technically not possible, well, no worries, also, like I said, I think that left clicking and holding it down entirely bypasses the engine bug. It also prevents you from reading the text 
but if you’re replaying a cutscene for the 3rd or 4th time you’ve already read the text