When I need to thin rims( 6,5x58R, 5.6x35R Vierling, .310 cadet, etc), I just chuck them in the lathe, with the rim bumping the chuck jaws( any type or even collet will work) and face them off from the rear. When I find the amount of reduction required, I set a carriage stop to make then all the same. I also set a cross feed stop to center the tool ( turned parallel to the "ways" to adjust initial depth by micrometer dial on cross slide) on the primer pocket and make the cut "out". So I move the tailstock out of the way, chuck the case, bump the cross slide against the stop, bump the carriage against the stop and lock it, make the cut, deepen the primer pocket with a Lyman primer pocket uniformer, radius the sharp outside corner of the rim with a file ( move the case out a little first to keep the file away from the chuck). Repeat the operations until all cases are done then chamfer all primer pockets by hand, doing it by under power can result in taking too much. On the first one, you can section the case to make sure it is not thinned too much. That is a long sentence, but when you are doing the work it doesn't take much time.