Why not make up a long dead centre shaft to seat in the rear of the chamber, with a lug attached similar to Brads wing gauge to act as a turning dog and fix the location of the centre.
If you are using a long bed lathe as I do, then a live centre in the muzzle and the made up dead centre/pilot in the bolt guide will hold it on centre, then I use a Milling vice on the lathe crosslide, with whatever I need, to cut or grind.
You should be able to use your back gears as a position lock, I made up an index lock years ago to use in gear cutting which allows me to set and lock at any angle.