I have done something similar, but not exactly the same. A few years ago I had an 05 Tundra 4x4 Double Cab, with the same 4.7L V8 that is in our rigs. I had the factory tow package and a towing capacity of between 6000-7000 lbs, which is on par with our 4Runners (the Tundra was a bit heavier). I was moving across the country for a military transfer (NY to WA), and towed a 24' enclosed car trailer all the way across the country. I will admit that I was overweight at 10,000 lbs in the trailer alone. I used a weight distributing hitch, dual sway bars, and a Tekonsha Prodigy electronic trailer brake controller. The truck pulled it beautifully. I kept it between 60 and 65 for the entire trip and never had an issue with sway, even from passing tractor-trailers. My milage for the trip averaged closed to 11MPG, with my lowest being around 7MPG while pulling up the east side of the Rockie mountains (I went across I-90). I even pulled the trailer up hill to Mt Rushmore so that the wife and I could take in the sights. (I had planned on dropping the trailer at the hotel first, but I was running out of daylight and took a chance.) I was only able to maintain about 20-25 mph up the steepest part of the grade, but I had no problems with transmission temps. I was monitoring several parameters with a Scangauge and the trip was made in late October.
The bottom line, your truck will probably do fine in the short term. Obviously, extended hauling at/over the vehicles GVWR will do a lot more wear and tear and result in more maintenance (either preventative or corrective, whichever you prefer).
My advice would be to lease a Tundra if you have the credit to do so, and can resist the mod bug. This will allow you to trade in before the added wear and tear from towing start to take a toll on the vehicle. Just make sure that you can accurately estimate the milage that you'll use and buy them up front. I just leased a new Rav4 for my wife with 16,000 miles/year. If we do end up going over for some crazy reason, my penalty rate is $100/1,000 miles.
