It's a crap shoot, however, I am certain you have a good chance on getting any decent side by side to shoot well with round balls due to the low velocity and such a wide opportunity for changing ball size, wads, thickness and style, crimp style and so many useable smokeless powders let alone 3 granulations and 2 to 4 different makes of black powder. Yeah- there are many more variables available for loading round balls in shotshells than there are for loading rifle ammo for any given rifle.
It may take some experimentation, but I am sure you can do it with just about any decent "pelter".
I would try the 12 bore first, but a 20 bore would work fine I suspect for shooting State's Side.
I would also chose a gun with a raised solid rib for dovetailing or drilling and tapping for a base for attaching sights.