I discovered this issue way too late into Jam 77 unfortunately so I doubt help will find me in time, but none of the tricks I've tried have worked. If the avatar exits to the next room facing the "flipped" direction, in the next room all flipping ends up opposite how it should be.

I do seem to be using the most updated version of the hack, as it in fact states it requires Bitsy 8.7 to run.

If anyone knows of a solution to this, I would be very happy to hear it so I can use this hack in future games.