As for most powerful, Geesh. I have a few of those unmentionable easy button pistols and per the manufacturer, when loaded with 80 grains it beats many factory 44 Mag statistics. And that isn't even max load.
I have never owned a Lyman pistol, but handled them. Seem very well built. Not available in flint, which is required for the PA three week flintlock season.
As for distance, all things are relative. When you can load up to rifle round ball stats, there is absolutely no reason why you are limited to 25 or even 50 yards. Though the eyes aren't what they once were, I can still hit a paper plate at 50 yds with a deer killing round ball that exceeds what some get from their rifles. With my scoped Hawkeye, I can hit the paper at 100 yds. I am getting better. there is no reason why that pistol is insufficient for 100 yd whitetail.
The lyman is limited by the configuration of the breech plug. It burns less in it's barrel length than a direct ignition system like an underhammer or in-line.
A 54 is capable of better burning because of the larger diameter. There is no reason why a 50 or 60 grain charge can't be utilized in a Lyman, except for possible stock weakness.
Incidentally, there used to be some stuff called "wood petrifier" Looked like water. Soaked into the wood and then hardened like epoxy resin. Soaking a kit gun stock in wood petrifier before final finishing might help strengthen the stock.