I used a jug of distilled water during my synthetic knot trials and it wasn't a hindrance outside having a gallon of water loitering outside my bathroom door. If I was suffering through hard water issues for an indefinite time I would consider it a legitimate option.
Keep in mind that in dealing with hard water the two primary approaches is distillation/de-ionization and ion exchange. The first pair are used to remove impurities from the water, with de-ionized water being considered the more pure product. Water softeners rely on ion exchange in which calcium ions are replaced with sodium or potassium ions, which, in the concentrations we are usually talking about, are less damaging and troublesome than calcium. In any event the Brita filters and similar products use filtration through an activated carbon medium. This results in cleaner tasting water, particularly if your water is coming from a treated municipal source instead of a well, but effectively does nothing to remove the elements that cause hard water.
Another long term and cheaper approach is to experiment with some different soaps. I know that Fine advertised that their soaps were formulated to perform well with hard water (unverified by me personally). I've also had good luck with Sterling's Margaritas in the Arctic while staying with my in-laws and I am of the opinion that their water is so hard that it might be usable as a building material.