No CLR! Seriously, that just sounds like the beginning of a 'wish I hadn't" story. Vinegar sounds like a perfect idea. Any natural or easily rinsed away acid should be good. Try rubbing in slices of lemon, for that matter. Buy a brand new scrubby sponge, rinse it out and have a good time.
Hot water with vinegar has always worked for me. I would also use a scrubber from your lfs, then if that doesn't work either...razorblade it! (Careful not to dig in the corners of the blade)