I wouldn't recommend carpet of any description in any function on a boat, except perhaps a small mat at the base of the companionway. It's a moisture magnet.
While it's labour intensive you could use closed cell foam as a "liner" (ensolite or even the sleeping pads used by campers) and cover it with a vinyl type material. Or you could "upholster" plywood panels and fix them in place somehow but that's tough to do with compound curves, of course.
Another tack to take is glue in some vertical furring strips and "plank" the inner hull (called the ceiling) with cedar or teak battens. You can use a layer of foam behind it if you wish, or leave it open-seamed and ventilating. This makes for a very nice nautical look.
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"