If you plan on using a roof box, don't forget that it will kill your (already not so good) gas mileage.

With only 3 weeks, the limited budget, and the "sardine can" situation, I'd seriously consider staying east of the Mississippi for this trip. If you want to do the western half, do that another year, possibly when you can take a lot more than 3 weeks, or when you have money to burn and can fly to LA and rent a vehicle out there for touring the West.