I think you will be fine. The Tundra is a very capable tow vehicle. I have a 2009 and my trailer is 6200lbs dry and between 7000 - 7300 lbs loaded to camp. Have towed to Florida from Ontario 2 times and multitudes of trips over the last 4 years. If I compare my Tundra to my '06 GMC Sierra the Tundra is rated for 1290 lbs payload and the GMC was 1700 lbs. My GM, weighed at the dump scales with 1700 lbs of junk squated as much as my Tundra with 2000 lbs junk. Just did not realize that I had laoded that much in the Tundra as I load them to give me a certain play on the end stops. Tundra also handled and stopped better than the GM even though it was overweight and the GM wasn't.
Not sure how the manufacturers come up with payload and other ratings but based on my experience you will be more than fine with a good weight distribution hitch even if you are 400 lbs over weight. I use the Dual Cam and have never had an issue.
Just my 2 cents. By the way not trying to say anything bad about the GM as it was a great truck when I owned it just trying to give a real world weighed payload comparison to try and alleviate your concerns.
