My plan right now is to use hot water to gently heat the case. Then apply force, either with weight or clamps, while it cools down. Just doing this a little bit I've already noticed the more drastic bends straightening out.
It will be difficult to deal with the warping though. For instance, the case around the arrow keys is warped to the point where they can't move freely without rubbing, causing them to stick.
I think this is going to be a slow grind with lots of little tweaks until I end up with something "good enough".
