It seems like you have enough depth to install a drop in panel of 1/4" thick material like plywood or medium density fiberboard. You could treat the panel however you would like to finish it before you install it to make things easier. You might be able to get the panel cut to size for you at a local store or hire a carpenter.

This unit does not look like something I would add damask to, why not just paint the whole thing if you must and then see if you need to change panels.

Before you consider painting or changing this credenza in any way, get some Old English lemon scratch cover and go over the entire thing rubbing the product into the wood with a soft (t-shirt) cloth and see if it revitalizes the piece enough to change your mind. It doesn't look bad as is.

Congrats on finding such an amazing piece! I like the idea of adding damask to the front of this piece. It will make it very original and truly yours!