I have a bunch of Lee Key Drive 7/8 oz. 12 gauge slugs that are intended to be loaded in shotshells with modern plastic wads.
The slugs themselves measure about .669 in diameter.
I don't know why folks tell you they won't be "accurate" if you put them into a plastic shot cup. IF the barrels are truly 12 gauge, and the slugs are made to shoot from a shotshell where they are loaded inside a plastic shotcup type wad....then they have every bit of a chance of having the same accuracy from your muzzle loader as you might get from a vintage, smooth bore, slug barrel on a pump shotgun. I have such for my old Remington 870 at at 50 yards with a Brenneke type slug, the cylinder bore slug barrel puts holes that touch at 50 yards. Beyond 75 yards the accuracy is crap...so IF I was hunting deer, I'd keep the shot inside of 50 yards. I have no idea what that Lee slug will do as far as groups.
Now depending on how the barrels were "regulated"...you may find you have some odd "kentucky windage" when holding that front sight bead on the target to get the slug to hit where you want..., but the same would be true for a vintage breech loading shotgun SxS shooting shotshell slugs.....
Muzzle Velocity is Muzzle Velocity, and the slug doesn't know if it got it's speed from smokeless powder or from Black Powder, or from a substitute for Black Powder. Of course the faster it's going the less drop, but on the other hand if like me and my "old school barrel" on a modern shotgun, if you check the groups at 50 yards you may have success. I settled on one specific load for my shotgun simply because it was the only one that shot well. You may have to tweek yours to get the same.
You should also try
unpatched round ball. .715 round ball will have a .007 gap around the circumference of the ball in your 12 gauge barrel. Use a plain fiber wad, or crush up some newsprint to form a wad upon loading, or you could use a wad of tow...and be sure to put a wad on top of the ball too to hold it in place. There is a reason why even hunters back when smooth bore flinters and caplocks were the norm, didn't use a patch. The patch folds different around the ball every time. In a rifle, the grooves not only impart spin, but also give a place for the patch to bunch up as it wraps around the ball, and it's a consistent pattern, every time. You don't get a consistent pattern with the smooth bore each time, so you actually may find it less accurate than a "bare ball".
The only other problem you have is that sometimes the inexpensive, plastic shot cups don't mix well with black powder, and especially with Pyrodex. (Pyrodex burns "hotter") They have a tendency to melt. I had a real problem in the past with AA brand shotshell cups and Pyrodex. Left a lot of plastic crap in my barrel that was the devil trying to get it out, and if you don't get it out it can create a minor obstruction. I had to use some very very old solvent with Benzene. Other guys have found brake cleaner will melt the stuff out.
LD