You need a way to remove ammonia, chlorine, and chloramines before the water gets to the tank. Assuming you are talking about the 55g tank in your sig, and based on EI the changes are 50%, then I would suggest getting a 25 gallon storage tank or bin of some kind. You can fill it up, treat it and let it age (which is also good for degassing) then use it for the water change. MUCH easier in the long run than doing the gallon buckets of distilled.
I think that if the algone removes nitrates as well, you will end up with another problem resulting in more algae. Better to find a good solution now!
EDIT: or maybe you don't need a storage tank. In-tank dosing is very typical with Prime.