I can see why you are having trouble getting a PT ,,24 to start We aren't really having much trouble in that regard apart from the kickback.Are you changing the complete motor including carby when you are swapping base? I often leave the carby on the frame when just changing over guickly. Saves undoing the bolts on the handle etc. If there is a carby problem then it will stay with the frame.
I had a side pull on this frame first. It was pretty tired but I don't think there was much difference in the way it pulled over and started No Kickback though.
A real mystery and a pity. PT s are much easier to come by at least around here.