Back to Leaky Waders, in all seriousness...
I aimed just above the shoulder at about 80 yards. No sweat with the terrible sights of that Sharps (no tang or peep on it, just a thin silver blade and a too-small notch). The things are pretty big. I did use the set trigger, so I could concentrate on the sights and then touch it off.
Using that rifle with black powder loads and bullets I cast myself was not about "period", it was about
process. Shooting gongs and having to hold two feet high for practice, sleeping out on the bone-chilling cold prairie in canvas tents with whiskey and wood stoves to keep us warm, taking almost a week, chasing a herd around, to get one member of the party after another into position, butchering the things ourselves in a barn, THAT is what made the experience.
What's the difference between gill netting and fly fishing? Process.
I'm not saying there's only one way to do something; I do, however, think that there are ways to get the most out of the buffalo experience. What I wrote above was meant to be a joke, through and through. I don't think I'm more of a "real man" for using one rifle or another. I just think I was enriched by the process that our group chose, and I am still grateful to the guy who had the crazy idea to begin with.
THAT, and only that, is why I'd recommend looking into it... I don't even own a buckskin jacket, and I've never been a re-enactor.