My experience towing with my Tahoe wasn't pleasant when trying to tow my current TT (which could be slightly heavier than yours). Take it for what its worth, but I own a 2003 Tahoe with 3.73 rear end and the 5.3 V8. Tow capacity per manual is 7,400#s. Empty weight of my trailer was listed as 5,880 and when I had it on scale ready to camp, I was at 6,700#s. Model is a 26tbss so was little longer than 26'.
When I was trying to tow this much weight with my Tahoe it was not enjoyable at highway speeds. Transmission wouldn't hold a steady gear and would do lots of jumping around. Felt I couldn't keep up to speed with traffic while on highway. Also, I felt the Tahoe was not in control of towing my TT. The TT pushed my Tahoe around to much, so for the first season I wouldn't take it anywhere but local campgrounds. I was using an old style Weight Dis. system and double friction type anti sway bars. I ending up buying a heavier duty truck which I now have control over my trailer.
BUT I will say, I did not trade in my Tahoe and kept it. I love my Tahoe as it runs like a dream at 120,000 miles. Tows my 4,500# boat/trailer combo around perfect.
My advice is get your trailer weighed ready to go before you make any decisions.