I've had some experience with deformed plastics and fitting.
The issue I was dealing with was a deformed door panel for my friend's car that I had helped retrieved from a junk yard. He had a gray interior and the junkyard one had a black one. He wanted black. Maybe not 100% applicable to your case but maybe its worth a try? This is what I did.
Tools:
Heatgun
Compressed Air Canister
A lot of time and patience, and a friend to help hold stuff down. I suppose you could use 4 clamps in this case. Make sure you pad the clamps so they don't make indents.
I attached one side (bottom left) to a clip on the door panel and had my friend hold it down while I focused on having the top right clip into place. I did the corners diagonally. I had the heat gun set to low and about ~6 inches away from the plastic, heating it as I slowly pushed it into place. I didn't just heat the side, I was heating the side all the way to the middle. So as to not get the plastic too hot, I would turn my air compressor upside down and spray to release some super cold air that would cool the plastic down in a hurry.
When I got the side I was working on to click into place, I had my friend hold that side down too, while taping down the side he was previously on. Then I repeated what I did until all 4 sides were clipped on. This unfortunately led to some gaps between the panel and the door. We taped down the four corners as snugly as we could and heated and cooled the whole door panel. End result? It worked pretty well. Not 100%, as you could still see some small gaps here and there, but it wasn't noticeable unless you were looking for it.
This may apply to your case as well. Just keep in mind, the part I was clipping the door panel to was a car door, so not too affected by heat. You have a chance of deforming the bottom part of the case if you apply too much heat.