I moved into a house with Hot Water baseboard or Hydronic Heating System with a Weil McClain.... boiler. The home is 6 years old.
I have nover seen so much dust in my life. I used to have forced air. It is just me or is it because my water is very very hard. We use a Water Softner. It that causing salt to evaporate in the air? the dust looks whitesh. We live in the North so the boiler is always running!
The heating boiler shouldn't have any effect on dust levels because it is a closed system. Hydronic heating water is never exposed to the air so it's not like it's evaporating and leaving trace minerals behind. The only place you'd get a buildup of the minerals is inside your heating pipes.
The same boiler may be producing your domestic hot water but the boiler wouldn't be introducing anything that would create the dust. If there are trace minerals (or salts) in your water you'd have the same problem with a seperate hot water heater.
One thing you could try would be to install a whole house water filter on the domestic water supply line (near your water softner) and see if that helps (although I suspect it won't make much difference).