jacob,
There are a couple of approaches you can take to conversion. If I were doing it, the first thing I would address is the door seal, since nothing else matters unless you achieve a nice fit.
There is a high probability that the door & case walls are a veneer construct-that would be in keeping with age & style of the piece. It also means it will be dimensionally stable when humidity is applied. I would suggest using a 1/4" mahogany veneer panel on the back of the door. Use a glue on edge banding or solid wood "picture frame" to treat the edges.
Then use 1/2"h x 1/2" thick spanish cedar strips, with 1/2" closed cell foam on the face to create a ledge that the door can seal against.These would be mounted to the inside perimeter of the case just kissing the door when it closes. You might test strip placement first using double stick tape, then make more permanent attachment once you are comfortable that it seals properly. A magnet upper & lower ensures contact with the foam.
The door seal pieces creates a 1/2" ledge that can hide the gap of the expansion space if you cover the walls with solid spanish cedar.One could also use the 1/4" mahogany again, which can have a nice tight fit.
Use spanish cedar for the shelves, trays, etc. add humidification & enjoy.
Very cool piece & project.
Cheers,
Bob Staebell