I'm totally up to speed now...and in case you're wondering, part of my interest in this thread is due to the fact that I've been lusting after the Camplite for a long time and have done considerable looking into it.
I'm thinking the Tundra will hardly know that Camplite is back there- it's considerably lighter than the Bigfoot to begin with, and from what I can see of the design better balanced to boot. The way they've got weight concentrated at/near the axles, combined with the lighter materials above the floor, reminds me of the way European trailers are designed. Many of those can be efficiently pulled with lower tongue weight ratios and by smaller tugs....and it may interest you to know that mechanical "sway control" is virtually unknown over there.
To get back to your original question re. w/d on the Camplite, I'm convinced that this "prohibition" by the trailermaker is for the protection of the aluminum frame...and since your Tundra has lots of available tongue weight capacity, I think a w/d would be more trouble than it's worth anyway.
Again, if "sway control" is your only concern, I think Camplite would permit the use of friction-type sway-specific units, which are NOT w/d systems. That having been said: sway is caused by a number of factors, the most important of which are trailer center-of-gravity/loading patterns and above all: speed. I've done a lot of looking into this subject, too- I'm towing (without mechanical sway control except brakes) at the very upper limits of my itty bitty tug.
A major trailermaker over in England has been partnering with a University in studying "sway" for many years. Their multiple webpages on the subject are most illuminating...if you're interested in their findings/recommendations,
here's a link.