Customer wanted a 7" deep box, she is painting the outside and lining the inside herself, a Cinderella's coach is going inside. She wanted a 1" wide gold moulding - not my cup of tea - looks like a cuckoo clock!
I decided to make two 3 1/2" boxes and glue them together, with MDF lining the outside for cosmetics and strength.
First I removed the plunger shown below, and its housing.

Then I replaced it with a few squares of foamboard, it worked great, 3 wedges stacked on both sides of each mitre. (Just an offcut of batten shown)

Then put the glass and the box in the frame and drew a pencil line around the box where it sat in the rebate. Along this line I inserted screw eyes (with the 'key' rings removed)

Then screwed these rings to the frame - see I told you there were uses for screw rings!!!!

The back was hinged for access, but the customer can also remove the whole box quite easily, by undoing the screws. This method is not very easy to seal but looks pretty. For something easier to seal, (remembering you can always silicone the glass and the box in) all you have to do is fire a framers point into the box and a staple over the point into the frame. Either method also works on stretched canvasses (instead of 'Z' clips) and for fitting liners into frames.