It's a sharps but made by pedersoli and the manual says smokeless modern non +p loads are safe for the action. I would be fine about 1300 fps.
Ok, yes you should be fine in the 1300fps range. Now here's where it get a little complicated. "Modern" single shots are considered to be guns like the Ruger No.1 and No.3 (and I believe the Browning reproduction of the Winchester Hi wall the B-78).
Your Sharps, is modern made, using modern steel alloys by Pedersoli, but it is not a "modern" design, it is a reproduction of the 1870s design, and while stronger than the original guns, due to modern steels, it is NOT as strong as the real modern guns like the Rugers.
there are 3 levels to current .45-70 handloading. I,II, and III, though some people reverse the order of the numbers
level I =modern smokeless powder loads that essentially duplicate black powder pressure levels and velocities.
This is what Pedersoli is referring to when they say "modern non +P" loads. Standard factory ammo.
The second level is heavier, loads with higher pressures, intended for top performance from the 1886 Winchester and the (new) Marlin 1895 rifles. These rifles are substantially stronger than the Trapdoor Springfield, and I think are a bit stronger than your Sharps. Think of them as .45-70 +p.
Too hot for the Trapdoor, and possibly too hot for your Sharps.
The third level is for max loads in the Rugers and certain bolt actions. Pressures can be in the 50,000psi range, WAAYY too much for even the 1886 Winchester and DANGEROUS in the Trapdoor Springfield. Too much for your Sharps, and possibly dangerous. The Sharps action is stronger than the Trapdoor Springfield but not a LOT stronger.
For your gun, stick with loads that stay close to blackpowder pressures and speeds and you should have no problems.
you can't safely make "magnum" .45-70s in the rifle you have, don't try!
I have some loads in an old Lyman book for the 552gr cast slug, they used Unique, 2400, IMR 4227, IMR 4198,and IMR 3031. I suggest you check for loads using these powders. I'm sure there are others (Reloader series?) that are suitable as well.