Polishing Mediterranean Vine Coral

Greetings Orchidians,

I recently purchased some mediterranean coral that is about 1" long
by about 3/8" diameter. They have a dull natural finish and I want to
cut them into smaller lengths, drill holes and then polish them. I
have the medium plastic media from Rio Grande and a flow through
vibratory tumbler, would this work? should I have a different media?
What has worked best for this material?

Thank you for any help,