usmc, I don't have a Tundra, but I looked at the specs of a similarly equipped Tundra to my F-150. Payload on the Tundra was a little over 100lbs less. Not far off, but already behind the curve if only slightly, but still comparable to the big 3 IMNSHO. So some of the thoughts/opinions things to do shouldn't matter too much based on brand and you could broaden your options a bit, so hopefully this helps.
To be perfectly honest though, I really haven't heard any good things about Tundra's from people who actually use them for anything other than a glorified grocery getter, but obviously ymmv. /Cue the person screaming "I do it all the time and you have no clue what you're talking about!" Just relaying my personal experience, I have no bias against Tundra's other than I really don't care for their looks.
I've got a Pastime camper that should weigh, if the manufacturer's numbers are even close to accurate, 1050 dry, and about 12-1300 lbs with all the options they gave me. With just the camper, myself, and the Jacks on the rig, with nothing else, I'm already overloaded, and as far as I can tell, this is a fairly light camper. If I take the jacks off i'm right at payload capacity, maybe a couple % points over.
In that config my F150 handles it fairly well, doesn't cadillac too much, and really doesn't feel overloaded. But, i'd like to tow my sailboat, it's not too big at about 2700 lbs fully loaded, but it's adding another 200 lbs tongue weight to the limits.
My F150 has the increased tow package capability too btw. Not sure what my exact GCVWR is, but from what I've read online, i'll still be under, though only by about 10% when towing the boat and camper and fully loaded with supplies.
I added the timbrens so far.. they are great with the camper on, and feels more "solid", though my sample size doesn't include highway miles yet, but should soon.
Advantages of the Timbrens so far are they are more affordable, and they are EASY as pie to install, I don't even really notice them under normal driving conditions as well, unless you hit something pretty hard then the back end feels a lot stiffer.
Negatives, with a little bit of weight, like 200 lbs of tongue weight and no camper, the timbrens are automatically engaged, and the rear end is STIFF. My boat bumps around a lot more back there without the extra weight to really soften the timbrens. Something to consider if your primary use is camper on, or camper off and towing. In my case primary use is camper off and towing, so I might see about shorter timbrens and airbags in the future to see if I can increase the "all purpose" ability.
I do agree with the people on here that say you need to go out and "try it" to see what happens. None of the manufacturer numbers are absolute, and as someone in another thread pointed out, many of the "payload" numbers are based on a certain PSI tire of a certain size. In my case the payload rating is at 35 PSI, but the tires have a max PSI of 44, so i've increased the pressure in them to about 40 to see if that makes a difference or not. I'm sure your Tundra is the same.
After my first trek, if the Timbrens and current tires don't cut it, i'll be upgrading tires, not to Airbags just yet, though again i'd like to do something at some point to make it better "overall".
Another thing to consider is removing the jacks. I've read many people state that a lot of campgrounds don't allow you to separate the truck. And i've seen lots of people that load it up and never separate it anyways. In my case if I remove the jacks i'm removing a good 130 lbs or so from the camper.
Anyways, hope that helps some...
Later
C