I would say there are a couple of points here. One is there will inevitably be an element of the symptoms being psychosomatic. I'm not simply writing everyone's concerns off as that, and it would be severely glib to do so, but there will be an inevitable element of it. People know that something fundamental has changed - their water - and inevitably there will be a tendency to blame every little ill on that known change. Taste is sadly something that you will probably have to live with. I have pretty soft water where I live and when I stay in a hard water area (which I often do) then I really notice the water taste; I'm more used to soft water now so I find I don't like the taste of hard water. However the more significant one, in my opinion, is simply the change; some people (and I am one) react to a change in water, which shouldn't be surprising since you are feeding a different mix of minerals into your body with the water. I spend significant time in different places throughout the year: seven months at home in the Highlands with soft water, two months in Redhill with very hard water and three months in Chamonix in the Alps with medium hard water. Each time I move to one of these locations I will have a mildly upset stomach for 2-3 weeks. This both I and my doctor largely put down to the change in water. It passes and you get used to it.
Chemically I simply can't credit the mix of hard and soft as being of significance; mix the two together and all you are doing is diluting the minerals in the hard water a bit more and yes hard water does tend to go pop in your kettle; ask anyone living in the south downs.
When I first moved into my village up in the Highlands the water supply from the village came from a small dam up in the heather covered hills. Our water came out of the tap the colour of weak black tea due to all the peat in it, sometime worse sometimes better. It actually tasted really nice having a slightly sweet flavour to it, however it did tend to leave tide marks when washing your whites. Many of the residents kept complaining to the council and eventually they switched our supply to a new bore hole. We don't have any limestone or chalk around here so this was still pretty soft water but much less so than before, which had the benefit of finally making it possible to rinse all the soap out of our hair. But now the older folk in the village complain their soup doesn't taste as nice as it used to...
Just some possible thoughts.