I agree with Chris, just cut all of the plastic heads off to remove the insert panel. Before putting it back to its position I drill all of the studs just enough to let in a small self-drilling wafer screw. If necessary a small washer would help to keep in place the screws. Some resin over the heads would give an original appearance.
What do you guys do about the mirrors on sunvisors? Some of them use the same method of a melted down plastic stud but it's much too small to screw it back together like you would a door panel insert. I recovered a pair for an early 2000s Honda Civic and had to eliminate the mirrors altogether. I do my best to save the mirrors whenever I can by tucking the material under them but sometimes I'm forced to eliminate them.
I use either screws or epoxy for the door panels. The high temp glue doesn’t work that well for that. But it does for the sun visors. Although I did have a picky customer that decided to take it apart and I had to use epoxy. I use 3M 04247 it takes a special applicator and tips. You have to be incredibly fast as the set up time is like 30 seconds, then you have to switch tips.
I prefer the self tapper screws. But sometimes there ist not enough material thickness. In this case just fix it with some hot glue poins but for the durability I use the black adhesive stuff you use for windshilds.
I've used products by 3M and Fusor made for plastic bumper repairs. They come in different strengths and speeds too. They aren't cheap, but They work great.
Norton structural adhesive number 5. You have to look at the type of plastic it's made of because with <PP> and other tpo plastic you have to use adhesive promoter to help it stick. I don't use the tip. I just squirt some out on card board and stir with popsicle stick and use the stick to dab it down in. I clamp the panel in place first.