You may find the discussion in this thread to be of interest:
Tumbler or Vibrator for finishing parts.
I use an orbital vibrator with ceramic triangles to debur and polish small aluminum parts. The debur is fine, but the finish is dull and mottled. Is there a better medium for polishing parts in the vibrator?
I visited a casting house about 15 years ago and they were deburring and polishing castings in a similar tumbler in one operation and doing a beautiful job. They let the parts vibrate over night. I didn't think to ask what they had in the vibrator.
That's a good thread, even though it seems like it wanders....
Compound is critical, and so is water flow, ... and you can regulate cutting action with water level if your machine will allow it.
I found good results with a plastic based media, but you can also get great results with ceramic abrasive free.
Mass Finishing Media Vibratory Finishing Media Steel Ball Burnishing Media
try round 1/4 - 5/16 ceramic balls or small diameter steel balls with a finishing compound.