You could try some brute force
What you need is some decent wood, something like 2x4 and some clamps
Then you need to place the wood along the most damaged part, clamp as hard as you can to try to force the bulge back in, it wotn be perfect and wont go all the way, but should reduce the bulge a bit
Are they "plastic" coated? If so you can go more extreme depending on your manual dexterity. If they are coated you can slowly cut around the top so you can pull it back slightly
Carve out some of the innards, fill back up after doing some clamping (clamping with some removed should allow a better return to original shape), then glue the top trim back into place
I would definately try the brute force clamping first, youc an often get 60-80% or so return to shape and that may be enough
