I couldn't find a faceplate for my old 12x37 anywhere so figured I would start making one. My manual said the spindle was 2 1/2 -8 thread but the major diam measured 2.356" so I decided to just match that with the female threads.
I have your exact lathe sold by Busy bee (purchased in '81). So hold on you your hat. The spindle is actually a 62 mm X 8 TPI!!! Yes it is! Someone here on the forum (I'm sorry I can't remember who) alerted me to this fact. I hope this helps!!!
I have a friend with the same lathe and he's made a very close mock up of his spindle to work as a go/nogo gauge... He's build several (perhaps 4 or 5) backing plates for it, and they are near perfect!
I have seen that even sloppy threads on chuck backing plates will still center up accurately, having said that, I personally make a thread gage for every lathe that I've had over the years, and also try to fit the unthreaded portion of the backplate for a close fit on the spindle.
I had a hard time deciding how to hold it so I could bore/thread it. A rotary table on the mill would have been nice but I don't own one. So I plunged the bit in between each gusset and turned it by hand so I had 3 surfaces concentric to the bore, so I could flip and run in the 3 jaw.