I didn't think the mattress on a Murphy bed folded. Or is that for something else? As for the plywood base, I don't see why that wouldn't work. I see a lot of platform beds with no springs.

Most antique Murphy Beds (left) folded and then rotated into a slightly oversized cabinet. Most modern Murphy Beds (right) simply rotate flat into a much larger cabinet fastened to the wall.

I expect that a replacement mattress for the antique would pretty much have to be a foam mattress, and that it would need to be cut to size. So-called "Memory Foam" would no doubt be a more comfortable choice than simple upholstery foam, but finding it and altering the size may be that much more difficult.

A plywood base shouldn't be much of a problem, and much less expensive than having the spring frame rebuilt.

Mattress for a futon might work, they get folded when put away

Thank you all....appreciate your help.