Azerbaijan Visa($100 US Citizen) can be picked up in Istanbul same day...good luck finding the consulate though...its right off the Subway...if you need, PM for directions.
It can also be picked up in Tbilisi next day...Georgia doesn't require visa for US citizens...
NOW the foreign registered vehicle entry is a bit dodgy, as they will ask for a deposit at the border, OR require you to park it at Customs within three days of arrival, IF you come from the main gateway from Georgia. There is another entrance in Northern Georgia that will grant you 10 days time in Azerbaijan, that my fellow travellers used as we were en route to Turkmenistan.
I'm not convinced there's ANYTHING worth seeing considering the hassle entering Azerbaijan...I personally would spend the time in Georgia...BUT if you must, bonne chance.