I think Franklin Armory completely missed the ball with the Reformation.
It's amazing that straight rifling is kosher (for now), but 5.56 is a total waste if the effective range is 50 yards. And I'm not convinced that the Nerf football bullet is a workable idea.
Pistol rounds, though, hold a lot of promise. Rifle caliber cartridges, and even intermediate rifle cartridges have a lot more kaboom risk if something goes wrong. Rather than a Nerf football, I think a shotgun slug is a more useful model. Pistol cartridges are relatively low pressure, and even a spicy pistol cartridge isn't going to be much faster than a shotgun slug. The effective range of a shotgun slug from an unrifled barrel is around 100 yards, which is about the range of a pistol caliber carbine anyways.
For ease of experimentation, I'd start with an externally attached rifled muzzle device. Just how hard is it to stabilize a pistol bullet with a goal of useful accuracy at 100 yards? Would you need a gain twist? Or would ordinary rifling suffice? How long would it need to be? Due to the square cube law, I suspect that the proportionately greater bearing surface of a pistol bullet over a shotgun slug might make for relatively easy stabilization. Something resembling a rifled muzzle brake would be ideal, but I suspect that it would have to be too long.
Once I'd have stabilization dialed in, if the device proved too long, the next step would be an internal device resembling a rifled choke.
If none of that panned out, bullet design would be next. A long bullet with a long hollow base that would be easy to cast, maybe powder coated to reduce leading. Like a Foster slug without the vanes. Or maybe with the vanes if it needs a little cushion when it hits the rifled device. Something with an attached base like a Brenneke slug would be too awful to hand produce in any significant quantity.
If none of that panned out, why not go full musket and fire a gosh darned roundball!?!?!
Except, I'd try to stabilize it with a backspin. Straight grooves only on the top half of the barrel, or maybe a roughened surface, or maybe even try some partial horizontal grooves. Roundballs tend to be around half the weight of conventional pistol bullets, so that would be a definite issue. Duplex loads also have their own issues, but I bet you could fit a triplex in a magnum cartridge. Probably need wads or disks or something between the roundballs. And of course lift generated by backspin might be an issue. Oh well.