Ruined balsamic salad dressing, how to recover?
Well, adding more of everything but xanthan gum would of course have the effect of diluting the xanthan gum. The problem is, it's possible that you used way, way too much xanthan gum (easy to do, the amount you need to slightly thicken a dressing is minuscule), so unless you've got a few 50-gallon drums of balsamic vinegar lying around, I wouldn't advise that you go that route. Instead, I'd suggest that you make a new dressing with no xanthan gum, then add the old dressing a bit at a time until you like the result.

As for finding an alternate use for (the rest of) your balsamic xanthan slime: I wouldn't. Xanthan gum is texturally quite unpleasant except at very low concentrations.