Coming in lare, as usual, if the 3 jaw, 4 jaw and faceplate are hard to screw on to the Mandrel, it sounds as if that is where the problem lies.
It may well be that the register has been damaged. A burr here wouldmake the fittings hard to screw on, and hold them out of position, and possibly out of square.
From what you say, it sounds as if your ER chuck goes on OK, and runs trues, which is puzzling when the others do not.
REALLY daft question, the male and female threads are all the same pitch and size? Ie you haven't been sold a Myford, with accessories for another machine? You should be looking at 1.125 x 12 tpi threads. From memory, i think that the register should be 1.250
Myford cognoscenti please verify.
Howard