I am not 100% positive on the boiling method, though I suspect it probably would kill some of the productive bacteria in water. I think you are fine just letting the water chill for a few days, it's distilled at that point. Unfortunately, some of the chemicals in our water don't disappear from being left out for a few days, but that's kind of out of your control.

You can get 5 gallons of reverse osmosis water for about $3.00 at most grocery stores. Not sure how big your OP is, but that isn't too too pricey for the upside it carries. Best of luck