May I suggest rigging up some sort of filter, so all you have to do is just vacuum the filter? As long as the inlet and outlet sides are isolated, you can use even a large cheap HVAC filter or whatever is easy to vacuum. Or maybe something as simple as it sitting on a rack with a sheet tossed over and tucked under with no concern for isolating the inlet from the outlet should let it circulate air without external dust shed and stirred up by the family being able to reach it.
It's already on a wire shelf almost at ceiling-level. You'd think most dust wouldn't reach up that high. But it does, after enough months pass.
We even put in vinyl flooring in the main room of the house -- which is a huge % of the square footage of our modest house. I hoped that would help with the dust buildup too.
But we have 9 children, and that's a lot of people in a house.
Our home is like a turtle, with the kitchen/dining room/laundry room/living room as the turtle's body, and the 3 bedrooms and "game room" as the turtle's 4 legs. That's it. No hallways, no side rooms, no basement, no accessible attic, no loft. Not even a closet in the main living area.