I have the same engine/transmission and my trailer weights can often be in the 8K-10K range. I use T/H mode exclusively when towing and have had no problems with heat here in the mountainous west. Also, my truck will shift to 6th while in T/H mode, if on a downhill grade. Also, I have never noticed the transmission "hunting" when in the T/H mode, downshifting to keep the RPMs up, yes, but not hunting for a gear. I am in the boat with those that say GM designed the transmission to do the work, so let it do the work for you.
