I think something else to consider is where you are located. If you read, most of these guys posting are west coasters. They travel through mountainous regions, and Like Enigma said, that is where he struggles most.
I live in Ohio, and have moderate hills, but nothing rediculous. I have an 03 Durango with the 230HP 4.7 with 3.55 gearing. I used to pull my race car all over Ohio, and surrounding states with it. I had a tandem axle trailer that weighed around 1800 pounds, and the car was 3100 at the time. Factoring tools, and other gear, I would say I easily had 5500 pounds of cargo being towed.
I never had problems with this arrangement. It would downshift on the hills, but was never out of power. I usually just presed the button to shut off the overdrive before I would hit the hills, no big deal. This way, it wouldn't try to take overdrive, and constantly upshift/downshift. Traveling at 65-70 on the highway, I used to see around 13-14 MPG with it. If you are traveling on roads that are not packed full of mountainous areas, I would think you would be ok. I have seen an inline 6 in a ford F-150 flareside tow an 8400 pound enclosed trailer all over the US for one season because someone had to.
Biggest question for me would be how much of a compromise do you think you are making using the burban to tow every other weekend, versus paying for alot more truck.