I never had the kind of accuracy with the new inlines shooting conical bullets as I do with the old style open breech plunger guns made by White Rifles. If I wanted to hunt and shoot conical bullets, I would put up with the extra fouling. I would save money shooting Triple Seven instead of BlackHorn (which I personally feel is not a good large conical powder in the first place), and look for a good White Rifle in good condition. It would be a .504 or a .451 depending on what and where you want to hunt.
If I had to get a new inline and shoot conicals, there are things other then lead conicals. Some of the CVA rifle we have been shown, shoot Thor Conicals well. One poster was shooting a new Tradition's Pursuit with Hornady conicals and again, did real well. I have some traditional rifles that shoot conicals real well. But these don't match your needs of clean breech and Black Horn 209. So I guess the best bet, and this is only a guess, would be a Knight Rifle. Since you want it clean, it would have to be a bolt rifle. Even though some of the older MK-85 were said to have shot conicals good with powders other then Black Horn 209.
But again, I would be willing to clean a rifle, shoot a different powder, and get a used White Rifle if I really wanted to shoot conical bullets. And we are talking large 460-500 grain pure lead conical bullets.