Using distilled (or deionized) water is going too far. This sort of procedure is used all the time in chemistry labs to get all the water soluble stuff out of a solvent that doesn't dissolve in water. There's even a "separatory funnel" to do the job but maybe not at the 5-gallon scale.
1948 3/4-Ton 5-Window Flatbed Chevrolet 34 Years. Now with a '61 261, 848 head, Rochester Monojet carb, SM420 4-speed, 4.10 rear, dual reservoir MC, Bendix up front, 235/85R16 tires, 12-volt w/alternator, electric wipers and a modern radio in the glove box.