Yes the devices can be "frosted" again by at least two different methods. There is a way to "paint" a white frost back onto the devices, or you can mask off the fields and then lightly sand or beadblast the coin. Eithe of these mthods will artificially frost the coin again, but they will be obvious and will not restore any value to the coin.
How about looking for a frosty Morgan again? There are plenty out there and it won't cost you too much!
There is one sure method to get rid of that overcleaned coin. Pack it up and send it to the USMint so they can make something new and not totally ruined yet. At least until your flea market nut gets to them. However, since you already have that coin, try the either Alcohol, bleach, Acetone or Laquer thinner for a few weeks soaking. Rinse with distilled water, place on a kitchen Window sill for several months. Might take on a little appearance of a normal coin but remember it will always be a cleaned coin. And if he really did use a Dremel, it may well have a scratched finish when you get the STUFF off.