I would have to go with the Sharps , the Spencer should have been in the running not the Henry,but even these had major problems.
The muzzle loading 58 Caliber U.S. Springfield using the hollow based mini ball
was able to do the following
The typical soldier loading and firing on his own could get about three shots off per minute. With the standard issue of forty paper cartridges, which is about a dozen minutes of sustained shooting.Then they would have to round up more ammo which was fairly plentifull
The Spencer fired a metallic cartridge. Including both carbines and rifles, approximately 150,000 of both makes were made during the Civil War.
In every major battle, the few regiments armed with a repeater ran out of ammunition at the first encounter. There weren't enough horses, mules, and wagons at the time to carry the additional ammunition consumed by the breechloaders. Battles were fought with each soldier carrying his own ammunition into the fray. Forty shots was the standard issue for about a dozen minutes of sustained fast and furious firing.
The Henry was underpowered for military use--about 14,000 were made during the Civil War. The Henry was modified after the War to become the first Winchester. A few single shot carbines fired the Henry 44 rimfire cartridge.
I think I would have stuck with a Springfield at least you would have amunition for the nest encounter if you made it through the present battle
.Graham