RE: shotgun or muzzleloading
I live in that situation. Where I hunt in Mississippi, a military reservation, the only legal firearms are shotguns and M/Lers. I chose an Encore w/ a 209x50 barrel. With 110 grains of 777 and a 250 grain shockwave it will cleanly take deer to 200 yards.
If I had to make a second choice, I think it would be a 20 gauge semiauto shotgun with a rifled barrel. My kids use this (and a cut down t/c black diamond most of the time) with partition gold sabots. At 100 yards it has solid 2 to 3 inch accuracy and I would feel ok using it to 150 based on the limited shooting we have done with it. If it were my only gun, I think I could practice with it enuff to feel comfortable to 200, maybe, maybe not, only trying would tell.
Hank