As others have said a 35' TT is too much for a Tahoe. I've owned several Tahoe's and they are just not built to handle that length.
My current TT is pretty much identical to your spec's and I towed it with a 2014 Silverado 1500 CC 4wd for a year with but I spent a lot of time getting the WD hitch setup perfectly. Even with that it would get a little interesting on the highway at times. The truck had enough power (5.3l w/ 6 speed and 3.42 gears) but I could never get it stable enough where I arrived at the campground relaxed.
Switched to an F250 and it is night and day different. I don't feel like the tail is wagging the dog anymore.