Good Quality Distilled Water???

RRL fluids, IMO.

Would water available through some aquarium shops be suitable? The shop where I buy my fish supplies has a large "reverse osmosis" filter system in the store.

I think the idea that you need distilled water is bunk. It is a result of the audiophile obsession to take everything to the extreme.

What's in your tap water, rocks, grains of sand? No, various chemicals in the parts per million range. I seriously doubt that a few molecules of chlorine or whatever left behind on the record will affect LP playback. Whatever detergents, etc. that are added to the distilled water to make a cleaning solution far overshadow those in the tap water.