I have a similar setup to yours and live in Florida where towing can be very hot. I second the suggestion to add oil and tranny cooling.
My 2013 GMC Sierra is nameplated with RPO (Regular Production Options) C5U for 6,800 lbs GVWR with the factory towing package which includes RPO Z82 Trailer Provisions, Special Equipment, H.0. which includes KNP cooling, auxiliary external transmission oil cooler; K5L HD external engine oil cooling, electric fan, and HD radiator; and VR4 trailer hitch, weight distributing platform. It also has G80 differential, heavy-duty locking rear, KC4 cooling system, heavy duty engine oil, and Z60 chassis package high performance, as well as oil and tranny temp readings on the magic mystery dash. (Boy, that was a mouthful!) (And for those who believe the Interwebs that you can't have Z60 and Z82, the glove box sticker in my truck shows both.) GM has apparently downrated these trucks to 6,500 lbs GVWR. The max trailer weight is 6,900 lbs. with these options and my rear axle.
It's important to note that GM rates the GCWR as *less than* the sum of the GVW and max trailer weight. That may also be true of Toyota.
The Fun Finder XT245 usually scales about 6,200 so I've always been a little nervous about being up at the upper limit. I use an Equal-i-zer weight distribution hitch with sway control and it makes a world of difference. My camper weighs about the same as the truck so it could push me around but it doesn't do that very much. Yours will weigh more than your Tacoma so there is a definite likelihood of the tail wagging the dog. I have a good brake controller. The truck has good service brakes but I like the control the trailer brakes give me. My truck also has "Powertrain Grade Braking" while in normal mode which keeps me off the brakes altogether on downhills. I keep the tire pressures up and check the trailer brakes often. It seems to work.
Florida Keys and far Northern Vermont
2009 Fun Finder XT245
2013 GMC Sierra