There are some threads on here about "drift boat floors" or maybe "walkaround floors"
Seems quite do-able. I don't think you'd have significantly more stability in a floorless raft than a cataraft...you're losing the flotation of the floor (displacement of water = floatation, even if the floor itself is not bouyant) and still really riding on two parallel tubes.
If you own the boat, it might be worthwhile. If you don't already have the bucket boat, I probably wouldn't undertake the project.
On the other hand, if you built it right, you could use it in either a raft or with cat tubes. The cat might be slightly more sensitive to weight...if you have a heavy bow fisherman, you'd get your front raft tube wet and pick up buoyancy. If you have the same heavy bow fisherman in a cat, he might pearl the bow of the boat.
DRE has one:
A few threads: