Fly and come back to a clean car
I've used these guys repeatedly when I need to fly somewhere - park in the business parking at the domestic airport (not that expensive if you per-book online) and leave your keys for the guys at the Car Cleaning Company to clean your car. They've got a range of cleaning options, all of which are pretty reasonable compared to other services, starting at $13.
I've always been really happy with the service quality, and the process of dropping your car off is made fast and easy by the friendly guy who has an uncanny knack or remembering your name even if you haven't been back for a month or so. Recommended highly.
What a great idea! Thanks for the tip!