I have recently picked up a Maynard model 16 in 38-50. When I insert a Winchester 38-55 case into the chamber and close the action there is about 0.012" gap between the head of the case and the standing breech. This seems to me to indicate a head space problem. I will probably be shooting this rifle exclusively with black powder. Should I attempt to find cases with a thicker rim? Or, if I cannot find them then have thicker rimmed cases made before shooting it?

Jeff is correct in that most of the Maynard proprietary cartridges for the 1882 model had rims about .070" thick. Modern cartridges won't always work when trying to get one shooting. You'll either need to make shims or buy special made cartridges from Rocky Mountain. You could possibly peen the rims thicker on existing cartridges but that is a tedious project.