The folds that were in the headliner out of the box proved to be very obstinate and wouldn't come out with the hair dryer. The heat gun worked better, but the extra heat turned the headliner glossy from just a little too much heat. Is there any way to degloss those areas or am I looking at painting my new headliner?

I think the gloss is there to stay. You need steam to get the creases out.