I've done about 12,000km's of outback travelling with our friends with their Sturt, and other than a little bit of dust near the door vent, they have not had any problems. The door vent is inline with the step recess in the floor, and any dust seems to settle there. It wouldn't be hard to put a canvas flap that can Velcro or press stud on to cover the vents if you needed. Their's is fitted with a scupper flap (a little pop up air intake flap) in the roof that is designed to create positive air pressure inside that they always open when travelling on dirt road, and it seems to do it's job.
A couple of years ago he replaced the mattress with a new inner spring mattress. Because the bed is a non-standard size, he had one custom made by MakingMatresses. He said it was a bastard of a job getting the old one out and the new one in through the door. Obviously the mattress must go in through the roof during construction.