The Uberti 1876 is proofed by CIP for black and smokeless powder, and is rated to be used at the same pressure point as standard .45-70; 28,000psi. They carry the proper proof marks.
The Pedersoli trapdoor Springfields are also proofed to this same level.
CIP is very stringent - no rifle gets out the door without being proofed.
I have done some work with the Uberti 1876, starting with finding a guy who owns a precision lathe who could thin some .45-70 case rims to the proper thickness, which was 0.063” for this particular rifle. After that I worked up some lower pressure loads conservatively based on data that the QuickLoad software generated. QuickLoad is a bit optimistic for straight wall rifle cases, so at best it provides a reasonable ballpark starting/max point.
I haven't tried using the standard 300JHP bullets. It's hardly worth it. You can get just as good results with a 300gr cast bullet.
You can get quite a bit more from this rifle than you can safely get from an original. With a bit of work you can equal factory .45-70 ammo ballistics, but with lead bullets instead of jacketed ones.
The Uberti 1876 is very fussy about OAL. Cartridges must be +/- 1/16” to feed properly. Choose the bullet that works best, and then trim your brass to get the right length for crimping with that bullet.
Send me an email and I'll send you the data. I've got several more loads ready to test when I get the chance.
Anyone who is really, really serious can spend the $$$ and get one of those RSI Pressure Trace rigs and glue on a gauge. It should be possible to do this underneath the barrel where it can't be seen, but you'd have to take the rifle apart a bit to do that.