What if you put some posts on top of the Mylar? Remove them where it’s easy and cut the holes smaller than the posts. It would be a bit more forgiving if they are not exactly in the right spot. Mount them over the Mylar. That would also help hold the Mylar down.
Haven’t really thought about it though to work out of the difference in height would make much of a difference, or f you don’t do every single one.
Alternative would be to remove all surface stuff and the overlay only has cutouts where there are holes through the playfield. Lots more work!
Food for thought.