What about swaging down a .375 round ball? Would the case mouth do that for me when I seat it?
If you were really cool, you'd paper patch two balls together into one projectile.
Kidding, but only sorta; multi ball loads can be fun and useful.
If you're interested and aren't already aware, for about $15 or so you can get a Lee push through die for cast bullet sizing that fits your normal reloading press. (I recommend choosing a size .001" less than you want, and then polish out the rougher internal section.) That's a quick & easy way to swage down that .375" round ball; I've done that a bit for various 35 cal rifles and 9mm. You'll want to put some sort of lube on it afterwards though, tumble lube is easy and so is powder coating. A big advantage to sizing down the larger ball is that it gives a little bit of bearing surface for the rifling to grab.
Otherwise sizing smaller and paper patching per your original idea is the way to go. I've had really good results with paper patched bullets and just wish it was a little faster to do in large volumes. Never tried it with a single round ball, but have made double ball loads for fun and that can work well, you just need to make sure the case neck is long enough to hold both, or handle the cartridge very delicately.
