Overkill? Yes! But $12k buys a really nice 2005 crew cab half ton pickup/SUV that gets 12-18mpg. That's what a 2009+ 3/4 ton GM 6.0L gets with far more capability and ease of towing, in far better condition. 2000-2005 Trailblazer, Explorer, Durango, Dakota, all get 15mpg like the half tons with bigger V8s! Why bother?
To significantly increase fuel economy, towing or not, means something like a late model mid-sized SUV, like Explorer, Acadia, Flex, or a diesel VW Touareg/Jeep Grand Cherokee diesel. But those are not $12k!