My solution is just not to look in there.
Actually, I do go through these compartments once a year and clean, usually when putting it away for the winter. I have not really noticed much of a layer of dust though, and we do travel a fair bit on gravel and dirt roads.
Haven't considered a filter, though anything with small enough pores to stop dust would likely negatively affect ventilation.
2017 Escape 5.0 TA (someday soon, I hope
2015 Ford F150 Lariat 3.5L EcoBoost
2009 Escape 19 (previous)
“Most folks are about as happy as they make up their minds to be.” — Abraham Lincoln