Ok, I am towing something similar, HTT with a dry weight of 3,625lbs.
Here are my 2 cents:
(1) I would not tow this trailer without the factory tow package, because of the legal concerns that were raised above. You can not increase the factory GCWR of 8,100 lbs (as dumb as it seems), no matter what equipment you install. That 8,100lbs will be your limitation. The empty weight of the tryck is around 4,100 lbs, so that leaves you with 4,000lbs (= 8,100 - 4,100). you now even need to subtract anything else in the truck: people, gas, any gear, etc. You will be at or below 3,500lbs.
(2) If you would load that trailer to the 6,200lbs mark (with water, gear, etc.), even a Tacoma with the factory installed tow package won't realistically be legal in most cases. The GCVWR is 11,100lbs, minus 4,100lbs dry weight = 7,000 lbs. Minus 6,200lbs for the trailer leaves you with 800lbs for gear, gas and people. Not much. I would not tow a 6,200lbs TT with my factory equipped tow package going camping (drain the water!)
(3) there is a third and fourth spec that you'd most likely be over at 6,200lbs: the tongue weight of 650lbs and the GVWR (1,300 lbs payload or so). Take off a 600+ lbs tongue weight, the weight of the WDH (mine is like 70lbs by itself), gas, people, ...
Sorry, I know it does not make too much sense that only the factory hitch allows you 6,500 lbs, but that's how Toyota specs it.
A good rule of thumb is that your towing capacity should be at least 1,000lbs higher than what you are actually towing because the tow rating is established by most manufacturers with the assumption of an empty tow vehicle and a 150lbs driver, nothing else. Then there is the "happy" towing guideline, that one says you should tow a ton less than rated (2,000lbs). That rule will avoid most "white knuckle" moments. :-)
I checked my trailer on our last trip, the trailer axles were at 3,560lbs total. Add 500lbs of tongue weight, and I am at 4,100lbs or so. I could take on a little more I think, but not much. That's the margin I like to maintain.