That's a lot of weight and a steep driveway. The only SUV that comes close is the 3/4-ton version of the Chevrolet Suburban and GMC Yukon XL, and even with these you'd be a bit over the maximum.
A Ford or Chevrolet half-ton large pickup with its optional towing package should be capable of this task. Among these, the F-150 EcoBoost has the highest towing capacity, 12,000 lbs. So this is probably your budget option.
Really, though, you probably need (or at least want) an HD (2500-level) pickup with a diesel engine. The problem with these: they aren't cheap. I don't know pickups well, so don't have specific recommendations of the Chevrolet vs. the Ford vs. the Ram. The Ford 6.0-liter diesel had some reliability issues a few years ago, but those 2008 and newer use a different, larger engine.