This is really out of my area of expertise, so take my reply with a ton of dissolved salt. I don’t know how much this filtered water differs from the reverse osmosis water you are now using. I am assuming it has more and different impurities than the RO water.

If this water is re-circulated through the process it may cause deposits in the condensers and re-boilers as the impurities buildup. And the metallurgy should be able to tolerate the Cl2. I think you suspect there could be problems in these areas. I think you should contact a water treatment company and get their advice and help in monitoring the water quality in the distillation unit. As these trace concentrations buildup it may also affect the VLE.