There is a less-than-lethal shotgun round that uses a hard rubber projectile that resembles a blimp. Fat in front, tapered toward the rear, with fins.
It doesn't spin, but from what I can gather, it's pretty stable in flight.
Of course, being a lightweight projectile the effective range is very short. How it would perform cast in lead at longer ranges is unknown. It would probably need to be slimmed down and possibly cast with a hollow nose to keep the weight down.
My ¼-scale Napoleon also uses 1.125" projectiles. I cast my own lead round balls, and am currently experimenting with scaled-down canister.
Something that's still in the "dream stage" is a finned stabilizer that would screw into for one of my cast balls. Making the finned shaft would be easy enough, the hard part would be the discarding sabot required to launch such a projectile.
If you did come up with something that worked, I would be interested in seeing the results.