To polish parts I use aluminum oxide wet or dry paper beginning with 240 grit. I then progress thru 320, 400, 600 and 800 grits. I make wood rubbing sticks of whatever shape is needed to polish all the surfaces. Final polish is with a buffing wheel.
My own preference is CLOTH backed abrasives,not paper.Before starting the polishing,
check the dimensions on the tumbler and the hole in the plate as well as the small hole thru the
bridle.If these parts and the holes they are associated with are not very close,in this case within
.003 I would not start the project.Also be VERY careful with polishing wheels because they can
"saucer"a hole and the end result is a bad job. Make sure the plate is straight as well.
Bob Roller