Murphy-bed mattress clearance is about 8 inches
We agree—we find this mattress to be comfortable and don't have any plans to replace it. I was going to respond sooner, but it took me until now to get out to the trailer to measure. The mattress itself is about 6 inches thick and we usually have 2–3 inches of bedding on top when we fold up. Your practical limit for a mattress would be about 8 inches thick because mattresses don't compress as easily as pillows and comforters. And that would require removing all the bedding except sheets and maybe a thin blanket when you stow the bed. I think the clearance between the bed frame and the wall is about 8.5 inches, so anything more than that you're not going to be able to close the bed, or you may put too much pressure on the latch.
It would be nice if there was an easy way for us to take advantage of some of the space behind the bed wall… there seems to be some usable space back there if there was a way to access it. 4–5 inches at least.