Wow OP! That is some water you must have. Have a shower then go to Las Vegas. You'll be so "active" that the fruit machines will pay out as you pass each one. Worked for Mickey Rooney See my note about his film "The Atomic Kid"
Excellent question if I may say so PE's word "weird" has to rank as a total understatement. So presumably no mini-labs where the OP lives as I cannot see a lab having to use distilled water in the kind of quantities that would be needed and no chance of Ilford moving its plant there any time soon
While I have benefited the science of photo-chemistry about as much as the Boston Strangler benefited door-to-door salemen, I cannot help feeling that, as you say, PE, there is something else going on here to explain it
Well, the Mercury, Cadmium and other heavy metals are sure messing with things but they are not the whole story. I'll bet that there is a whole range of organics in that water as well and they might be doing something to your paper. OTOH, what do I know about water like this?
There is more to this than meets the eye. Most of these agents would have FOGGED the paper, not left it clear.
Distilled water is cheap enough in most of the US (I understand this is very different in the UK and elsewhere) to just not be an issue. It's $0.79 a gallon at the local Kroger. It's a bit more at some other local grocery stores but still less than $1.20 per gallon at worst case. I routinely use it for all my developers even though I've seen no indication that I need to, just because it's cheap insurance. I haven't used it for stop, fix etc. because my belief has always been that those are less critical. I do mix Photo-Flo with it for my final rinse.
I once bottled liters of dehumidifier water to use. Within a few weeks there were blooms of something growing in every bottle. Brand new dehumidifyer so it was all fresh from the air. Algae grows in mine regularily so I have to keep a cap of bleach in it.