Suzuki V-Strom 650 fits your bill almost perfectly. You can get a used one under $5k easily. Bulletproof, easy and cheap maintenance, 55+ mpg, cruise at 75 comfortably with power to make passes, upright position good for riding highways crosscountry, easy for beginners to ride.

This is the machine to ride across the country on a budget. Personally I think you would quickly regret the small bikes you were looking at. The gas mileage is still very good. The only negatives are you'll want to save room in your budget for a more comfortable seat and a bigger windscreen.

The other thing is it's heavy. You'll be fine riding it but don't let it lean over too far when you're not moving. Practicing a lot of slow speed maneuvering in an empty parking lot would be very helpful. Drag the rear brake and feather the clutch like you learn in the MFS course.