Just picked up on this thread.
I don't think that the fact that your softener was wrongly programmed would have effected what came out of the tap. Once all of the calcium ions have been exchanged for sodium ions the softener won't add more sodium ions to the water. Anyway, being programmed for harder water simply means that the unit will regenerate more frequently than necessary, so all you were doing was wasting salt by flushing the resin before it was needed. You can't 'over treat' the water.
Anyway, the reason for the post is to say that whilst it is always said that too much sodium is bad for fish, I was never able to find out where the balance was between too much sodium and too much calcium. Many years ago I therefore started to experiment with mixing my source water and softened water (all my water goes through the softener apart from a drinking water tap at the kitchen sink).
So, for approx 20 years I have been doing water changes using water that consists of about 25% 'softened' and 75% source water. I have kept all kinds of fish and never had a problem and one big benefit is that even at that level of dilution I get hardly any calcium deposits in the tank any more. I don't measure it scientifically, I just run both taps into my bucket and guess at the flow rates! All my fish live long and healthy lives and plants flourish.
One thing you must never do is use water from the hot water system as this is likely to be very high in deadly copper. In older houses without a softener the risk is lower because the pipes and water tank are likely to have become scaled so the water doesn't come into contact with the copper. This won't happen with a softener though, so the danger from the copper pipes remains high - I see you use water from the bathroom so I wonder whether that's the problem?
By using water in the kitchen, the 25% that I use from the softener only passes through a couple of inches of copper pipe, and the untreated source water only goes through old pipe which is likely to have the protective scaling. I bring the water up to temperature by adding boiling water from a kettle.
Some tap water conditioners will neutralise copper, but not all, and at normal doses I'm not sure that would be enough to treat water from a hot tap unless the product specifically says that it's intended for that purpose.
Good luck!