Wow I haven't heard of that combination towing that heavy yet. My salesperson towed the same travel trailer as mines with a newer Tahoe with the 5.3 and 4l60 trans but everyone at the campgrounds or on the rv forums have big blocks at the least and mainly diesels. Let me know how it works out. Are you beefing up the trans with shift kit or cooler?
Run it as-is. I'm going to be towing my 9100 pound camper with my stock Chevy 350/5.7 and 700R4 transmission. With the 6.0 and the 4L80E you have, you shouldn't even know the trailer's there.