OK...I have a 2007 Tundra with the 5.7. I've used it to tow my 2002 Sunline TR-180 (30' overall length) that I just traded in, and I'm fairly sure that I was towing around 8,500 lbs. The truck handled it ok, but I also have a Hensley hitch....good weight distirbution and absolutely no sway. While the truck can handle it, I think I would be putting quite a strain on the truck to take it to the Rocky Mountains....which is on my bucket list. We just purchased a Winnie 2201DS with the intention of downsizing (just 2 of us) and getting the total trailer weight to less than 7,500 lbs. So...if the weight you gave is the GVWR, I suggest that you need more truck....3/4 ton or bigger.
Check out the Minnie Winnie floorplans. Will the 2451BHS meet your needs?
http://winnebagotowables.com/minnie-floorplans
There are some 28-30 foot trailers out there that check in around 7,600 lbs. or less if you look carefully. We chose the 2201DS because of the quality of the trailer, amount of storage, and outdoor kitchen. It was the best of anything we could find in a 2-3 hour drive from our house.
Good luck on your search!