As this is the BP page, I'll assume that you are thinking of using what would otherwise be a BP cartridge with a nitro load.
The black powder cartridge rifle association here in UK, for obvious reasons, does NOT use nitro, so joining a similar group of people in Canada is obviously not for you. You add that you are not competitive, however, I'm willing to bet that that would change if you got to a range where other shooters are having at an 800m steel buffalo. Somehow, being the only person on a range has never appealed to me, apart from the fact that here in UK it's not permitted.
I'm sure that there ARE loads for the good ol' .45-90, 110 and 120 that can be emulated with nitro, but in spite of being a shooter for well over 60 years, and definitely not recoil-shy, I wouldn't care to be shooting prone behind any of 'em. Launching a 500gr projectile at 1750 fps - or so - can really blow the wax out of the ears.
Guns to look at are definitely the Pedersoli Sharps - right at the top of your budget, and available in .45-70, -90, 110 and 120, or the Remington Rolling block which is, TMK, only as a .45-70 cal. My own rifle is a Uberti Model 1885 in .45-70 and it definitely has lost out at anything over 600m to the bigger capacity cartridges of the same calibre. Remember, too, that these huge bullets are LEAD, not jacketed, and you'd have to find a rifle that would shoot such bullets. TMK, none of the current crop of long-range BP rifles actually do that, mine included, although it IS nitro-proofed.
Seems to me that you have offered us a bit of a conundrum here, so I'll let wiser and more experienced heads than mine answer you better.