So I might be going out on a limb here, but why not just get a dehumidifier for your house? You should put it in a separate room for your frogs so it doesn't suck humidity from your frog's tank. But the water left in it is distilled. If you have a basement or something that would work fantastically. You wouldn't need to worry about buying distilled water anymore (or as often anyways).

Another option is to get a reverse osmosis system (not cheap though). I'm not sure if it's actually distilled but I'm assuming it would remove enough mineral to be used in your mister.