I am about halfway through the book on Hinson. So far the author doesn't go into enough detail for rifle aficionados on Hinson's rifle. What I read so far is that it would take a special kind of bullet not a round ball.
From other stuff that I've read, none of Hinson's other accessories remain; such as bullet mold, powder flask or even the bullets themselves.
I was trying to find something which would give us the exact bore diameter, type of rifling and twist rate.
The question as to whether he used a patched round ball or conical bullet can be answered if we know what the twist rate of the rifling is.
If he commissioned a rifle with a fast twist then he probably used a conical bullet.
Having cast lots of minie balls myself, I can tell you that it's difficult to get one that's perfect. Casting a conical bullet that I can wrap paper around is much easier. Besides the common method of paper patching back then was to use two strips of paper laid cross-wise over the muzzle. The bullet's base is pushed over the intersection of the paper strips and down the muzzle.
If he wanted to use a minie ball for a projectile, the 1858 Enfield rifle at that time with the Pritchard ammunition was very deadly. It would be far easier for him beg, borrow or steal an Enfield for his deadly target work.
IMHO, if he used a conical bullet it would have be one of the slug variety that was used in the long range target rifles at the time.
I may be wrong on some of this as I have not got past the part of the book where he is planning his revenge.
If I were wanting a rifle like him, so far I would also want a heavy one 17-18 pounds of the target variety. In that day, the slug guns were often a lot heavier almost twice as heavy but I still need to maneuver with it.
Additionally, if a search was made of my home then a 36 pound target rifle would be a dead giveaway and implicate me. So a compromise of weight needs to be made. Since I'm going to use my horse to transport me to the AO, a 17-18 pound rifles would not be a lot to carry unless I hiked long distances on foot.
The slug guns of the day, often used a false muzzle to load a paper patched bullet. Again, having a false-muzzled rifle could implicate me in my planned carnage. Besides it's not necessarily needed as I'm trying to hit a man-sized target out to 300 to 500 yards not the x-ring of a paper target. Hinson's rifle doesn't have a false muzzle.
Whatever technical knowledge that I am lacking on barrel twist and type of bullet a gunsmith could could have up for. I could probably buy almost any .50 caliber rifle with a slow twist rifling to shoot patched round balls but I want one that has a twist rate for conical bullets.
So far a .50 caliber muzzle loader that is a little on the heavy side but doesn't scream long-range-slug gun isn't going to attract a lot of attention or necessarily implicate me as long as I'm not caught with conical bullets. Regardless, I'm not planning on getting caught because, like Hinson, I would have known the terrain better than the Yankees and I pick the time, location and targets when it's advantageous to me. Never play another man's game and in his backyard.
The only way my theory holds any water is if Hinson's rifle has a fast twist rifling in it. Whoever produced the barrel at that time would know that in order for long heavy bullets to accurately hit the target, the rifling needs a fast twist.
If the rifle has a slow twist, then Hinson would have been using patched round balls. Are they capable of hitting a man sized target at 300 to 500 yards. Yes, but not as well as a good paper-patched slug.
I reserve to right to alter my theory after I finish the book or get more information