Not sure how I missed this thread originally. Very interesting topic. I do have a few thoughts on it.
First stage of filtration: A custom built or commercial cyclonic filter, mounted on the bumper (or in the bed of a pick up) with a snorkel cap that also incorporates its own cyclone.
Second stage: As has been posted (I did not read the entire thread), a cyclonic snorkel cap on a duct that feeds a cyclonic pre-filter for the engine air intake, mounted in the bed of a pickup or on the bumper of a car. Same thing for the passenger air, but feeding an external CBRN filter system.
While the cyclonic filter will get most of the ash, you still need additional filtration, so a filter box using K&N filter elements is placed in the duct from the cyclone to the regular engine air intake. Carry a cleaning kit for the K&N filters, plus spares.
Do a similar system for the passenger compartment air intake, except run it through an external CBRN filter system after the cyclone and K&N filter stages.
Also as has been stated, do not forget the radiator. This requires even more air flow than the engine, so filtering will probably not work very well. However, something similar to a cyclonic filter can be made to divert the air flow downward sharply to force as much of the ash to drop out of the air stream before it gets to the radiator. A large box mounted on the front bumper in front of the grill with large downward sloping plates would force much of the ash to drop down, as the air turned back upward on its path through the radiator. (This can also incorporate radiator ballistic armor, too.)
Do not forget the windshield. If you drive slow, it will minimize scratching. But if the ash fall is heavy, there could be an accumulation, requiring the windshield to be cleaned. But running the windshield wipers will just scrape the sharp ash across it more firmly, scratching the windshield more quickly.
Adding a set of air nozzles that can be used with compressed air from an onboard compressor system can be used to blow the ash off. It can be attached to the windshield wipers, if a lift mechanism is added so the wipers do not ride on the windshield, but a quarter of an inch above it. This way, the moving wipers can keep blowing the ash away.
Just my opinion.