Regarding your comment "One thing I have heard about the filter and box fan solution is that pushing air through a good filter can overly stress the fan, since it’s not built for that, and be a potential fire hazard. Has anyone else heard that?"
I have heard that certain filters may damage the unit. But I would guess that a dirty filter also does damage to the unit!
I researched and use a quality filter rated 4 out of 5 for air flow in my apartment. Apart from catching certain things, I have also noted much less dust with it...and that means less dust going back into the unit
I have read that one should check with the manufacturer for the maximum MERV rating allowable for a unit.