Re-form and conserve combination caps

[senhoragua]

I have quite a few combination hats that I've acquired over the years, and they came to me in various states of disrepair.

 

All have the standard internal wicker frames each are bowed-out. I would like to reform the frames (somehow) to make them more presentable. What would be a safe way to do this? I thought I might get some butcher's twine and thread it between the two cap screws and draw the twine in every now and again to not stress out the frame too much.

 

The peak on some seems to have flattened due to incorrect storage as well. Would cut plexiglass or cardboard be the suggested means to prop it back up?