First, I seriously recommend you stop tasting/eating your polishing cloths...
For someone who actually knows what they are doing, the bench lathe (proper polishing machine capable of using larger buffs, with variable speed) is much preferred to something small and hand held like a Dremel or Foredom. In the hands of skilled professional, the bench lathe is hardly a machine for butchering cases - it is much more likely to give you a better and more even result than a hand held small diameter tool.
Refinishing includes the application of many different surface textures (it's more than just making things shiny) and is a skill set that has to be learned just like any other. There are many poorly refinished watches out there - I see and fix them often. Many are done by people who do this for a living, but have either never learned to do it properly or just don't care. Many are also "home" polishing jobs that have been poorly done - I recommend leaving the work to skilled professionals...
Cheers, Al
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