Distilled water has a pH of 6.0 ... it's not pure water.
I would simply use a product with HCl hydrochloric acid and some humic acid ( as a buffer ) ... you need more acid. The kH and gH of your tank water is whats resisting or neutralizing the acidic effect of the distilled water. My distilled water I have sampled out here also has a kH of 40 mg / liter... so each addition is a bit counter productive if a pH drop is your goal.
Keep in mind as change tank water out with distilled water and your kH and gH drop so will your waters ability to buffer changes in pH ... you could end up with the pH bouncing everywhere ... a touchy system to maintain ... also your fish need time to adjust to drops in hardness.
Why the change ??
My tap water has a pH of 7.8 and a kH of 180 ppm and a gH of 300 ppm ... I can add a gallon of distilled water to 14 gallons of tap water and the pH won't budge at all ... in time you can change the pH with more and more distiiled water but is this what you really want ?? Very soft acidic water ??
Soft water has it's share of problems.
Good Day ...