Forest T
I believe if you have a Hawkins your barrel twist will be something like 1 in 66 and is not condusive for conical bullets that you are wanting to shoot. This is a round ball barrel twist in a muzzle-loader.
I used to own a TC Express that had a 1 in 32 which was more friendly to conicals and did find some from Parker Hydra Cons. He sent me several conicals to try out that he paper patched with a very thin paper. I shot his 580-gr pp conical quit well. According to the rule of bullet weight vs barrel twist I was told this would not work. Well I was shooting targets at 600 yards using a front Lyman 17a globe sight and a rear vernier tang sight... not your standard barrel sights.
But if your going to paper patch a conical it must be under bore for starters so you can wrap it correctly. The patch should wrap twice around the conical or bullet for a proper patch. Now remember a proper conical or bullet for paper patching will have NO lube groves. If it does this can cause the paper to stick to the conical bullet during flight instead of releasing as it exits the barrel.
Heres what I would do.... your going to have to start with an undersize diamiter conical bullet. The closest thing I can think of to .50 cal is .45 cal. Check your conical bullet diamiter that you need to wrap to and try to wrap the .45 cal conical up to what you need.
You will need to use a wad under the conical, one that is lubed, because with paper patch bullets you have no lube groves to carry lube down the barrel, if you don't you will have tremendous fouling.
I wish you well with your efforts, I quit muzzleloading after I got into loading my 45-70 and 45-90 with BP, but I paper patch my bullets still.
Take care
Jon