Working on those callouses on your finger tips it sounds like. If you
have any old inside ring sticks: they are sometimes handy for making
a holder. Just saw off the felt and make your impression in the wood.
Use bar soap or what-have you to create a little resistance if it
slides around to much in your depression.
You can order MX wheels for grinding. For your purpose, it sounds
like the medium, or the fine, would work well; and comparatively
quick. They also make split laps in MX. If you don’t have a split lap
machine you can mount on your polishing shaft with a 1/2" arbor, in
place of the tapered spindle.
If you want to make a split lap machine use an old washing machine
motor. They are meant to operate vertically. Just mount it kind of
like a steering wheel faces you in a car. The shroud is nothing
special; something a good sheet metal person can crank out for you in
less than an hour. I would guess $35 to $50. You should position a 3"
duct on the side for your collector to hook up too.
Don’t try the dryer motors for vertical use, they don’t last. Dryer
motors are great for polishing, however. The mounting plate attached
makes them quickly serviceable for jewelry polisher.