Hi Gary,
I can't answer for JLC but honestly my opinion is not really good news for you.
I don't think JLC would do it for free. Even if your watch is still under warranty, this kind of stuff would not be covered by such warranty IMO.
Regarding cost, I don't think you'll get an estimate before you send the watch. Quite probably they'll have to disassemble the watch to repolish, so it would not be cheap.
Except if you can't keep it like that for a while, I'd personaly wait until next service to get it polished.
Cheers
Dje