I use a 3/4 ton Chevy conversion van for ours. It does well with the 5.7, and the price we paid was well under your specified dollar amount. If you want a van (they are great, you can haul all kinds of stuff inside) probably a Chevy 20 (or 2500) series van, or a comparable Ford or Dodge window van, LONG wheelbase, but without the extended body hanging off the back would do well for you.
Of course, the Airstream owner's tow vehicle of choice for many moons has been the Suburban. If you can find one of those for the money you have to spend, it would be great, too. Just make sure whatever you buy has sufficient tow rating for your Overlander.
Meddle not in the affairs of dragons, for you are crunchy, and taste good with ketchup.