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I would just use the distilled water the distilling process makes it pure removing the harmful minerals.The reverse osmosis system is usually very good but to know for sure it would still need to be tested. I used a reverse osmosis system a few years ago that took the TDS down to around 3 ppm Total Dissolved Solids, which is very low. It was a new system to remove minerals from undrinkable water (it had a very high content of iron. My system had 3 pre-filters and the reverse osmosis filter. It worked well for us at the time but now it would need new filters and there a little on the expensive side. Fortunately we live in an area where the tap water is excellent and very drinkable.
For a complete flush we use a long blue RV filter from walmart. Goes inline on the garden hose.
Drain system completely including block drains.
Then fill with coolant and distilled water.
Some flushes we do would consume 10 - 20 gallons and buying jugs of that is just ridiculous.