What we perceived as dust was in fact fine particles of salt from the softened water, settling out all over the house. I finally remembered that the kitchen sink is supposed to provide unsoftened water, and began filling the humidifier there. Problem solved.
It took a week or so to learn that we were still getting "dust" settling all over the house, even using unsoftened water. Instead of salty dust, the new dust was the hard water's mineral content.
The problem was the type of humidifier we were using - a "cool mist" type. It was spraying tiny droplets of water into the air in a stream that resembled fog.
Containing mineral or mineral plus salt, the water would evaporate but the water-hardening mineral was left behind as "dust." Subsequent online investigation revealed recommendations to fill the cool mist humidifiers with distilled water, which has little or no mineral content.
We consulted with neighbors who have had humidifiers operating for years with no dust problem and learned they had evaporative humidifiers. We've stopped using the cool mist microspray machine and purchased an evaporative humidifier. It is both larger and more expensive, but does not require distilled water.
The new machine wicks tap water up into a matrix through which room air is pulled. Evaporation will leave the mineral content behind as it does not evaporate. The stream of air leaving this new humidifier doesn't resemble fog.
Cleaning the mineral stuff left behind in the machine will be a periodic chore that is likely to be unpleasant. We've yet to do it as it appears to be more or less monthly. If I remember I will report how ugly the cleaning process is, after we've done it.
