I know that you were saying you were considering using distilled, but for others who might be thinking about it, topping up with unboiled tap water is a prime cause of chlorophenolic off flavors.
Make sure you remove the chlorine by boiling, using metabisulfates (powdered or campden tablets), or charcoal filtering (very slowly - too fast and the chlorine makes it through).
Chloramine is even harder to remove - boiling doesn't volatize it out. filtering must really be slow but metabisulfates work better. 1 half of an aspirin sized tablet will treat about 10 gallons of water.
HTH-