It sounds as if you want a CVA Mountain Rifle. These have been out of production for many years, but the .50 caliber versions show up pretty regularly on the used gun market. The .58 (actually .575") Big Bore Mountain Rifles were produced in much smaller quantities, but you see them up for sale occasionally. CVA also made the Big Bore Mountain Rifles in .54 caliber, but these are really scarce. The Big Bore Mountain Rifles have a 1" x 32" barrel and no cap box on the buttstock, while the standard CVA Mountain Rifles have a 15/16" x 32" barrel and a German silver cap box. I have one of each, a .58 and a .50. I am small of stature and pretty thin, having lost some muscle mass with aging, but the Big Bore .58 balances very nicely for me. The CVA rear sight looks funny, but I get a very good sight picture with their standard factory sights. The Big Bore CVA Mountain Rifle handles well.
After these went out of production, they were very hard to find for a number of years. There seem to be more used ones for sale now than ever before. It is sad to say, but I'm afraid a lot of the original owners have either "gone under," or have seen the writing on the wall and elected to downsize their collections.
A .54 caliber Lyman Great Plains rifle would probably meet your needs. People who have them seem to like them, and they pop up for sale pretty regularly. The biggest complaint you hear is that they are heavy. Eh? Maybe ten pounds? The original plains rifles were most often in the 12-13 pound range, with many even heavier.
If you really, seriously want a mountain man rifle, you'll be looking for a late, fullstocked flintlock longrifle.
Good luck!
Notchy Bob