Water softeners are added to eliminate the problems caused by calcium and magnesium in water - soaps don't work well, shampoos don't work well, etc. Softeners don't remove the iron found in lots of well water. Not every builder of houses knows the best ways to do water plumbing, and not all inspectors are competent. I believe it has been established that water softened using KCl instead of NaCl is still very bad for plants, so just switching to the different salt isn't going to solve the problem.
If I had to do some replumbing to get the water before the softener "ruins" it, and the point where I could do the replumbing was only 15 feet from the location of the tank,I think I would try very hard to run the new water line over to right behind the tank, so I could semi-automate water changes - just open a valve to add water. During cold months I would think about doing smaller water changes more often, to avoid having to heat the change water at all. Adding 20 gallons of 40F water to 40 gallons of 80F water gives you 67F water - not great but probably no problem for most fish.
Tom Barr's non-CO2, no water change method, is for very small amounts of fertilizers being added, so there is no chance of building up too much of any fertilizer in the water. Since I'm using CO2, my plant growth rate is much higher, so the plants need a lot more fertilizer to support that growth, which makes me dose enough to have to do water changes to avoid build-up of fertilizer in the water.