For best results in your Sharps replica, I would try either 22.0 grains of Alliant 2400 or 36 to 38 grains of IMR 3031 with your 500 grain cast bullet. If you keep the velocity to about 1100 to 1200 fps., you will essentially duplicate blackpowder load performance without the smoke cloud and cleaning requiments associated with BP.
Recoil will be noticeable, but tolerable, with the those loads and your rifle's steel buttplate. Accuracy will probably be best at about that velocity level also. Heavier loads will beat you up and turn your shoulder purple...ask me how I know!
Your rifle can handle heavier loads, but should not be used with the extremely heavy "Group 3" loads that are listed in some sources. Although it has a very strong receiver and breechblock, the firing pin design is not considered suitable for extremely heavy loads.
I had a Pedersoli Sharps and a Shilo Sharps at different times and used the 22.0/2400 load with good results in both, but be careful to inspect your charged cases in good lighting conditions before seating bullets to make sure you don't inadvertently double-charge a case.