1983 Ford Mustang Starter replacement

I have installed 6 (that's six!) Re-manufactured starters into my car in the last six weeks. They act perfectly for the first three or four starts, then, they will not grab the flywheel. They start making whatever kind of noise and might. Catch and start, but then just spin. I have been told that during this period, (1983), that there may have been a different head on the starter that meshes properly with the flywheel and that that is not the case with current re-man's. Is this possible and if so, where do I find the proper starter? Tired of sinking money into it with same results. Replaced solenoid, cables, battery, alternator, regulator. Everything working good except starter. Pulling my hair out. Any help?