What ended up making a difference for us, is buying a portable industrial air scrubber, of the kind construction/remediation sites use to clean the smoke and dust (and mold, and asbestos, etc) they’re generating out of the air before it gets vented outside (see e.g. https://a.co/d/01lTtyuZ); and plumbing this machine into our apartment in reverse: putting it out on our (covered) balcony, with it exhausting the “scrubbed” air into the apartment. (I made a little sliding-door shim of the type people use to pipe portable AC units outside, just with the hose on the other side.)
Generally works great. We run it on a very low speed, so it’s surprisingly quiet (no louder than other fans we have for air circulation, and a more pleasant frequency because of the large diameter of the fan it has inside.) The pre-filters get absolutely caked with exhaust and road dust after ~2wks, and start to let through an odd stench at that point, so we’re actually replacing those faster than even is recommended for the industrial use-case. But the actual main HEPA filter inside the unit seems to last longer than in industrial usage.