So just as a side question, is there an easy way to match the joint and shaft collar on stitch rings like these to where you don't have to keep trimming and and taking the cue apart over and over again until the rings line up? I've looked for an answer and obviously there's a process but I can't find it anywhere.
Math?
After assembling it the first time, note how far off you are.
a10 pitch thread moves .100" forward for every full turn. I don't know what the pitch/spacing of your rings would be, but humor me and say it is 12 index's around the ring, or 1/12 turn for a full offset. That would equate to taking .0083 off one face.
If I was 100% confident in my dials, I'd take off ..008". If i was less confident of dials, and where tool tip really is at the point of first cut, i'd take less. As long as the part being faced is not removed from the lathe, (nor the cutter) after first cut the dial should repeat/be accurate for small increments.
If the spacing is closer, you can estimate things like 1/2 or 1/3 space out of time. In example above, if increment was only 1/3 space, amount to remove is less than .003".
If you estimate the increments based on what setting you used on the dividing head (or index) to make the rings, be aware that like a gear, the full space counts from a valley to a crest, not top to top, or valley to valley. Edited: since the features on a stitch ring are not always the same size; a better way to say it is: from the edge of a feature (black, say) to the same edge of the next same feature".
I'd still creep up on it, but with a little estimation, you should not overshoot and have to try again several times.
smt