Here is the problem with this plan. Distilled water is going to cost about $1/gal. you will be needing about 13-14 gals of it at the outset. Then, assuming you will change 50% of the water weekly, you will need 6-7 gals. of distilled. At $1/gal that is about $6.50/week x 52 weeks a year means about $338. Consider getting a small RO/DI unit. The DI resin will remove the nitrate which is an ion.
I have a 75 gpd portable 3 stage ro/di unit that cost me about $125 years back. You can still get it for the same price on Amazon. Before you buy it, try the distilled to see how it works for you. If it doesn't do the trick, then don' buy the unit.
https://www.amazon.com/Portable-Aquarium-Filter-System-Membrane/dp/B004N7QUXW?ref_=ast_bbp_dp
