[Mean Daddy]

The one I bought is like the one on the right. Problem is its engraved glass so I’m afraid of forcing it.

[Pollard]

I would try the refold and if that doesn't work, another freeper's suggestion of finding a woodworker. They can either build new sides from scratch or just extend the back but inset it a little from the sides so there's no visible joint and if hanging on the wall, it will give the appearance of floating off the wall surface by an inch of or half inch. Something like below. (bottom in pic is the back of the case that gets extended for more depth)

The second method could be a DYI thing if you're handy. It would also be an easier and therefor cheaper method to pay a woodworker to do it.