I tow my travel trailer with a 2000 Suburban, 5.3, Sumo SuperSprings. It's 5800 dry. I figure, without water, I'm still plenty over 6,000 Lbs. Yeah, it's slow going and I drive it easy. I have looked at 2500 series Suburbans, Avalanches, etc.. With the 8.0 they are a little cheaper but, I don't want that engine. The 6.0 versions can be quite expensive, considering year and mileage. I keep kicking myself because I saw a 1996, 2500-454 V-8, 4x4, low miles on a lot a couple of years ago reasonably cheap. And it was as shiny as a new penny. I passed on it. That 454 is a hoss and would have been a great vehicle for towing. Not much of a daily driver mind you.. I keep passively looking. And I haven't ruled out a 3/4 ton Chevy or GMC van with the 6.0.
BTW, the chassis does fine. No complaints with the WDH. And, if you could ride around at 3200+ RPMs the power would be fine..