I just hired a college kid to do some of my inside doors with a strong shop vacuum and a wide brush head. He did about 60 doors, the hallway floor, all window sills and horizontal surfaces in one day. It cost me $12 per hour plus a replacement vacuum filter, total about $110. If you keep up with the dust, you shouldn't need to wipe it with a wet cloth. (unless maybe you're in a humid area where the dust turns to mud)

For the outside doors, we wait for a really hot day and hose them off with one man on a soapy long handled brush and another being careful with the hose stream (more like a mist actually). The hot day helps evaporate any moisture that may make its way around the door.

Those waxy dusters wouldn't work on my doors, they would fill up with gunk so quick they would be useless and just smear.

If you feel you must still wipe with a damp cloth, I would at least vacuum them first, you'd remove 80% of the dirt and be left with a much easier job.