With the much longer barrel, the bounty hunter is so front heavy that it pretty much requires a rest under the barrel to utilize the range and accuracy the longer barrel offers. The other thing, is the straight barrel. Whether a significant change in balance can be made by tapering the barrel, I don't know.
There is a video floating around on-line of a guy here in PA bagging a doe with his flintlock bounty-hunter. Some states have a minimum barrel length requirement. So the kentucky style pistol does not qualify for hunting in some states that require a 12 inch barrel. Here in PA we have a 50 cal min. for deer, but no barrel requirement.
There are a few cheaper traditions and CVA long guns with pistol grip stocks. I bought one to cut down into a pistol. I figure a 12 inch barrel is plenty. The whole rifle cost me $100.00. I will cut the barrel and cut new sight dovetails. The gun already has the ram rod hole, a hooked breech and barrel wedge system. I would move the rear sight to the breech to gain sight radius.