J. Browning made his first machine gun from a 94 Winchester 30-30. He used a paddle to catch the gas from the muzzle blast. The paddle mounted to a pivot attached to a simple OP rod worked the lever. This was his first machinegun.
Why couldn't you design a multi-barrel muzzle loader like a Gatling system. Use the Browning Paddle system to a OP rod to activate and fire a full auto muzzle loader.
Bear in mind that this would then be an NFA class weapon and illegal.