As much as I love my Ballard rifles, and would choose them over most others; I think the finest single shot 1800's American designed action is the Remington Hepburn. Not only is it extremely strong, but the side lever has huge advantages over any of the underlever designs from other makers.
Being able to open or close the action by means of the side lever will allow a hunter to load and unload without rolling the rifle to it's side if he's got any interference below. It also allows the shooter to open/close the action without changing his hold.
And then there's the sheer strength of the Hepburn design that's as strong as any other American made single, and stronger than many also.
I love my Ballards, but I'd still choose one of my Hepburn rifles for a strictly hunting rifle.