I am in the middle of restoring a DE Simpsons.
Had the same raised inserts on the couch and also the 2x, 3,x 4x, 5x and 6x and a few others.

Pulled the mylar with freezing, came off ok.
I had a fair bit of damage on the lower half of Bart and Moes bar in the top shooter lane so I decided to do a full resto, big job!, lucky I have PF pics and an artist mate!

If the rest of it is OK I suggest you get a 12inch clamp and a block of wood and clamp the inserts down and add some 2 part epoxy to the back of the inserts to hold them in place.
Rough up the insert lip and the wood to get the epoxy to bite, use a screw or a nail or something small and sharp pointed.

The inserts lift mostly due to heat from the lamps underneath so I change all insert lamps to LED's for this reason, plus they look way better.

Deal with the mylar as needed, pop and heat, inject and clamp, etc.

Most of the repair stuff I learnt from VIDS thread.

Good Luck and let me know how it turns out if you can be bothered.

Cheers,
Matt.

Mine has very minor lifting, to the point it's only noticeable on the 2x, and since that's not really going to affect any shots, I let it be. What was more concerning for me was the wear where there wasn't mylar (drop locations for yellow/green wireforms, Moe's Tavern, Waterfall, and kickout/VUK holes).

Hopefully your machine is clean in those areas because color matching and touching those up was a T.A.S.K!