I tow with a Tahoe as well. I dont feel comfortable recommending over 25 feet ball to bumper on the trailer with a Tahoe due to the short wheelbase and the rather soft coil spring suspension. It also porpoises even with stiff sway bars for the same reason- the suspension throw is long and the springs are designed for ride comfort. I have a 24' trailer that weighs 4300 lbs, and it has been rather fine for over 6k towing miles. If you need to choose a brake controller I recommend the Prodigy P3 with the GM factory wiring harness adapter- it's easy to install and use.
The newer generation Tahoe has the integrated frame hitch that isn't as strong as the older generation and isn't field upgradeable, so watch the tongue weight too. A 6900 GVWR is going to give you near 1000 lbs tongue weight in real life.