Our lathe came with a snug fitting nose on the backplate, but the chuck was not running true , no matter what key was used to tighten down on test pieces, from, 8,10,12,16,19,25mm samples. So I skimmed the chuck register on the backplate itself, so the flange face had now swash run out, and then took 0.1 off the register. Remounted the chuck, with the screws lightly nipped, and put in the 12mm pin, indicated it to zero near the chuck and looked at it from 30mm out. It was fine. Snugged the screws, and checked all the other common sizes that I use and it was really good, within 0.02mm over the range with 12mm being my zero. I don't do cuts heavy enough to be moving the chuck, and anything with interrupting cuts I use the 4 jaw chuck.
To assemble very tight fitting parts, a very light smear of castor oil , will make the parts easily assemble. The down side is that castor oil can turn to a gum and then make the parts hard to dis assemble. There are some other oils and greases that allow tight parts to easily assemble. One that surprised me is the lube grease for DMG Moori machines grade 000 grease. Really expensive in NZ, but is around 30 pound for a 1 litre bottle that will last a lifetime.
I can not underestimate the cleanliness required when changing chucks or face plates on machines . The screws needs to be really clean and free of any dust, grit etc. So a little time to make sure everything is very clean, really pays off in the long term.
Jason has nailed how to make a test plug for making a new backplate to fit your lathe. To try and get the very close finish, if the compound slide is set at a very shallow angle like 0.5 deg, you can use the movement on the compound slide to make the very small diameter changes. There is no issue with polishing to final size, once you get down to the last thou or 0.02mm on diameter as you sneak to the final size. The register is better to be slightly in the tighter side rather than the looser size. My chucks and backplates came with a relief on the first 3 4to 4 mm of the length of the spigot, so about 1/3 is relieved slightly.
Neil