Half the dust just goes into the air and resettles elsewhere. It seems like I am making the situation worse.
How can I wipe the dust in a way so as to avoid just pushing it around so much?
I did some web searches but none of them seem to have much helpful advice on this.
Vacuum it. My friend has a Roomba that does her whole house automatically. I thought those things were ridiculous until I actually saw it.
Also, as someone said, air filtration should get some of the dust out of the air. That is healthy for breathing. If you don’t mind the noise, you can make a powerful air filter from a box fan and 4 furnace filters: look up “Corsi-Rosenthal box” for how to do that. Otherwise you can get a smaller one.