Alternatively, one could book a Flight+Hotel with very cheap hotel and then book separately with preferred chain. It seems one need only check in to/check out from the BAH hotel but can occupy the other.
This is somewhat convoluted, but the idea of hiring the car and then leaving at the airport, as has been suggested) does not sit well with me for liability reasons.
Cheers.
The times I've done Flight+Car, I've picked it up and parked at hotel (with one exception, where my plans changed to a further internal flight and I became a non-pickerupper!). In some cases for just getting to/from the hotel and local stuff, in one case a Transylvanian road trip
