I don't think what you want exists. There are lots of muzzleloaders in .45, .50, and .54 available for your budget, but I would consider those deer calibers.
You could take Elk with a .54, I'm sure, but if I were going to be chasing moose, I would want at the very least a .58, and if I had my 'druthers, I'd be holding something even heavier. Guns like that are much more rare, and usually more expensive, though you might get lucky and find one in pawn for well under what it's worth.
Of course, this is with patched round ball in mind. If you're going to shoot conicals, you're talking a totally different ballgame.