I'm a little late to the party, since he already traded up. But yeah, the 5.3, although a great little engine, can't handle the duty of towing something that heavy. The 07 Suburbans are big and heavy on their own!
I have a 38' Travel Trailer, ~10,500 lbs. fully loaded, and we used to live in Southern WV (Beckley) right off I64 & I77. There is a hill about 10 miles outside of Beckley on I64 called Sandstone that brings trucks and heavy vehicles to their knees. It's 5 miles long, starts out at 7% and the last mile turns into 7.5-8%.
When we moved down (Jan. '05), I had my '89 3/4 Suburban 4x4, 350TBI, TH400, 3.73, 285/75-16s, and when I towed my 16 ft open car trailer with my '70 Camaro, I hit the bottom at 80mph and slowly slowed down to 42 mph at the top, and it was just about to downshift into 1st gear.
That's when I knew that she just wasn't enough anymore. A couple months later is when I got my '04 2500 4x4 Suburban with the 8.1 and 4.10s. And oh my, it was a night and day difference. Now with this Suburban, on my way home from a race one weekend pulling the same car and trailer (I figure at about 5500 lbs.), I had to stop at the bottom of the hill, right before it started (a carsick passenger), and when I started out, I kept it to the floor until it reached 80 mph at about 1/3 of the way up. That kept me grinning for a while.
Anyway back to the camper. I never got to tow up that hill, but I came down it with the camper when we moved back home (Eastern Panhande of WV). There are 2-4 mile hills all along I64 towards I81 that are up to the same 7% grade (Sandstone just being the mother hill), and I towed the camper (which was prolly around 11,000 lbs since we put more stuff in it for the move) around 70 mph and maintained at least 65 on everything but one hill, which brought be down to 61 mph. All of the longer hills took 2nd gear revving about 4000-4200 rpms to maintain the speed, but that Suburban and those 8100 Big Blocks are freaking animals. Too bad Chevy doesn't offer the 8100 in the Suburbans anymore. The 6.0's are comparable when not towing or towing smaller loads, but not when towing those heavier loads. You just can't beat a big block or diesel for towing.