Is it a 4x4 or 2wd? If you do a gear swap, the 2wd will obviously be about half the cost of having to do a 4x4.
We started camping with a pop-up and a 94 Caprice Wagon or 02 Silhouette. In 02 when we bought a 23' hybrid that had a GVWR of 5000# we towed it with the Caprice. It did have the 5.7L LT1, but it didn't have the towing package so it had 2.56 gears and electric fans vs the mechanical fan.
With the exception of the tranny heating up in stop and go city traffic, it did just fine towing. On steep hills where the torque converter wouldn't stay locked in third, I could go to 2nd and tow at 55 or 60mph because of the 2.56 gears and the tranny would run cooler.
You are definetly going to want an auxillary tranny cooler added. Is it in your budget to swap gears? If so, why not start with the cooler and if the 3.08's don't work then swap gears. I am guessing you will have to tow in 5th and 4th might be best. But in comparison to the 4L60E you will still have an extra towing gear.