I thought the same about the foam when I looked at it. The foam is actually the problem and the rears don't have foam and they show no signs of lifting off. I am going to have to do the Pass side eventually, but I have to do the Drivers side cause it's really bad. Can't install it the way it is.
I am actually changing the top of the doors too. It's not as hard a job actually as doing the vinyl insert. This is going to be time consuming and require lots of patience. I have three of the cards pretty much done. There is some gunk on them I am trying to clean off, looks like dirty hands were on them. They look OK. Fortunately I have the two door panels and will be able to take the tan panel off, remove the insert and put the tan panel back on the door so (it will open

) I can take my time with this. When I get it done, hopefully, then I can remove the top from the tan panel and glue it to the black and be done. FYI--anybody switching out top panels be aware you don't have to cut the tabs, just peal the glue off with a flat blade screw driver, clean it up with a stone on a dremel then pop the top off. If you cut the tabs you will have nothing to glue to. This way they just pop on to the new door card, glue and your good to go. It takes a little longer but is not difficult. Take your time
I am going to see if I can get it cleaned up this weekend, maybe check on some material, but I think you maybe right about gluing material, could be messy. I guess it would depend on what I find and how dense it is. I won't hold my breath on that. But I will look, I think the spray glue would hold it. Especially without the foam.
I have pix of doing the tops of the doors, but don't want to mess with your thread. It's tied into this project sort of and it's not as big a deal as I was led to believe. Just don't cut them off, really!
Look forward to your pictures and thanks
Tracy