Decided this morning to go with using a pieces of the extra baffle material to back the door. Little bit of a process to bend correctly but here's a picture, might be hard to see but the bottom piece basically folds over the top piece.
Also good tip on checking Ebay for the latches, found 2 for $17.50 each.. 4 left if you want some! They're -32 so I'll have to build the buttons up a bit to get them to go through the metal backing and the glass.
I went back and forth between using expoxy or some fantastic 3M adhesive stuff I have. In the end put the pieces together with the adhesive. Won't know till tomorrow how well it worked.