Distilled water is expensive, are u saying run distilled water through whole of flowering.This is not a permanent solution because it would end up being costly over time .... You can buy distilled water for a week or so. Here's what's going to happen a few weeks after your plants are put into flower. Calcium needs will go through the roof. Things should begin to balance out.
I would continue with the epsom salts mixed in with your feed and then do what you can to keep from adding more calcium to the soil (filtered or distilled water).