The White Mountain Carbine has a 1-38 twist so they should shoot conical bullets well. I do not own one. But have read a lot about them. That price to me is at the end of the expensive side, but I guess if you want a short carbine for close quarter shooting that would be a good rifle.
I would personally look for a Renegade, Hawkins, or Lyman Trade Rifle if I want to shoot a lot of different things, like roundball, sabots, and conical bullets.