I guess I would try to find a place outside safe from amimals, or hang them and let the meat rot off, unless your in a hurry. It would take a year or more.
I have heard of burying them also, for a year, and the worms and decomposition happens, to clean them up.
Hollowfox- do you plan on carving it as a whole rib cage or single bones?
I don't know if I would cook them, because they get softer and darker, where you let them go naturally, they stay lighter. (Although I have boiled skulls in bleach water to whiten them.)

I have been thinking about deer rib cages myself. I thought I could somehow hang them from a frame of somekind and play them with drumsticks or something like that. Kind of like a bone xylophone. I think I would have to epoxy the bones into the spine bone though. I really want to try this idea. It came to me when I saw a perfect one on the side of the road, already decomposing.
Peace, Rustic