Cyclonic pre-filter is an excellent idea but probably wouldn't be off-the-shelf ready to install the same day.

The standard during Mt. St. Helens time was to add an extra foam filter around the car's standard paper filter. Amsoil makes them. Then you have to clean and re-oil the foam regularly.
Looks like the ShopVac arrangement.

Drawing air from the car's interior only means that you'll use the car's interior as your dust filter for the engine. Might be kind of hard to see out.

Modern vehicles will run on the correct mixture until there's not enough air to run because they use oxygen sensors in the exhaust to adjust mixture. Carburetors in the pre-computer age would run richer and richer as the air filter clogged.

The more filtration the better because volcanic ash is even worse than beach sand for the engine to breathe because the ash has very sharp edges while sand has been worn down.
You really, really don't want to drive in this stuff if you want your car to last more than a trip or two.

You also want to remove the ash immediately as it tends to set like cement when it gets wet.