Eesh. In my walkthrough at least the game started seizing up after the first training session with Batgirl in civilian clothes finished, in the main town square. When entering any other building, including the chinatown map, the game would recover and play at normal speed.
The disparity seems to continue regardless if is the day/night cycle.
Additionally, I am not sure if seeing the grandmother was the issue, but eventually I was locked into a loop where I was 'too tired' to go outside in the hero costume, but 'not tired' to sleep, thus ending any potential progression.
Oh, and if you attempt to use the door to the building to the left of the church the game plays a sound and the door just sort of.. moves around on it's own.
Sooo.. yeah, you've got bugs, chum. Seems entertaining so far.
In terms of suggestions, I'm somewhat of the reverse of a lot of other comments here-- I'd like there to be a way for the hero(ine) to end up a smoking hottie shemale/fem and give as good as she gets, rather than just being a submissive lack of substance. Maybe a combination of the two routes?
Either way, best of luck with this, looking forward to seeing it progress.