20 gage with a solid slug down a rifle barrel is hard to beat.
Would be easier and cheaper to have a custom mold made to simulate the .577 Minie sans hollow base than develop a new gun. Make the slug fit grove diameter. Lube it then load over fiber wads.

I just use a muzzle loader here in our state of Illinois.

If you made a pump action dedicated Minie ball shooter it would be a rifle and not a shotgun. Thus would not meet Illinois deer hunting regs. IMHO. However if it was a one of a kind wildcat whose shells were 1/8? shorter than a standard 20 gage. Who would notice. Call it the 20 outlaw. Not really my cup of tea. Would make a good episode for one of those silly TV shows. They?d have to fit the round into a Saiga auto loader of course.