Blooie, the closest size balls available from Track of The Wolf are .575, .580. and .595. Given your rifle's land-to-land diameter of .594 and groove depth of 0.015, I would think a .595 ball would be a bear to load even with a thin patch. So I'd try .580 balls and a thick .022 denim patch. If you find a source of .590 balls (or have a mold made) that size would be perfect for .018 pillow tick patch.

Can't help you much with conicals. But you really need to determine the rate of twist of your barrel before getting too deep into them.

Generally speaking, except for a perfectly fitting minnie, conicals will not do well in a slow twist barrel designed for balls. Minnies are lubed and not patched. Conicals are generally not patched. But "paper patched" and cloth "cross patches" can work quite well in barrels with suitable groove depth (usually shallow) and twist rate.

We'd sure like to see a picture of that cannon.