Distilled water contains no minerals, but will pick up anything in the atmosphere- C, N, P, O. You'll have to use calmag and then adjust the pH if needed, as C, N, and P can form acids in the presence of water.

Just mixing your nutes won't re-dissolve insoluble salts.

You should be using hardwater formulas if your water is that hard. Your background ppm is outrageous; check the GH hardwater formula or the Canna one shown here:
Canna Hydro Vega 1Ltr Hard Water / Canna Fertilisers / Two part nutrients / AquaCulture Hydroponics
*I've never ordered from that site; link is for the product description*