Have you looked at the tires,tires,tires forum here, or the Avalanche forum? I'd also see check people's comments over at www.tirerack.com - where you can search by vehicle model & maybe someone will mention that he trailers.
If it was me, I would go with the LT tires. I don't know what your tongue weight is but if its high, you may get a sizeable bulge from your original equipment tire sidewalls. OEM tires are almost always a compromise at best and its rare that replacing them with the same tire makes sense. I like strong sidewalls on LT truck tires and always had good luck with BFG All-Terrain T/A tires with the Tri-Guard sidewall. Its possible that there are other tires now with sidewalls as tough as those, so check around. The last thing you want when you're trailering on vacation is a flat from a torn sidewall.