Sounds like the OP has got it figured out...aside from owning a toyota (but that's my personal opinion working here...)
Anyway I've been down this road. 24' enclosed with car inside. Trailer is 3500 lbs even. Car + tools and junk another 3490. Right at 7000 lbs give or take a few. I used to pull it with a 2003 F150 Lightning; and it pulled "great". Plenty of power, brakes decent, etc. In '13 I traded the Lightning for a 2003 F250 diesel. I thought to myself, I'll be fine pulling on the ball-it's not "that" heavy. And for the most part, it's not. And I was used to pulling with a 1/2 ton truck (a real 1/2 ton not a 3/8 ton), and it was fine for the 9 years I owned it. Read on.
In early '14 I found a smoking deal on an equalizer hitch setup. Having never used one, I was reluctant, but for the price, I couldn't pass it up-figured I could flip it and make about $200 on it. Decided to try it. Once set up properly, it is literally a daylight and dark difference from pulling on the ball only. Even with the F250, when an 18 wheeler passes you at, say, 75 mph, you felt it. You had to steer. On a windy day, forget it. Park and wait for the wind to die down. Then I put the E2 on. HUGE difference. MUCH more confident, in every aspect of towing that trailer. Yes it's a pain to set it up properly. Yes it takes longer to hook and unhook the trailer. But those are minor inconveniences compared to potentially taking out someone's rig, or mine, or worse taking someone's life, from an even mildly ill-handling tow rig. I even looked the F250's towing capacities. 12,500 lbs. But when I looked at the factory-installed hitch, it showed 600/6000. I'm like what in the world? I read further...600/6000 is on the ball only. 1300/13000 weight distributing. And now I understand why there is such a big difference....
There is SOOOO much more to pulling a load behind your truck then just hooking on and going. Trust me, I see stupid crap all day every day; ranging from leaving the ramps down and dragging them for miles (and not knowing....?????) to not latching the coupler and taking out tailgates and back windows on expensive SUV's and trucks, to pulling a trailer that has a 2 5/16" coupler on a 1 7/8" ball, and wondering why the thing is rattling. No lights (none at all, not even installed), lights inoperative, no grounds, no brakes, bad brakes, junk tires, huge holes in wood floors, bent and broken FRAMES, axles welded to the frames solidly....etc. Just amazes me, but anymore, it's entertainment, because 99% of the people that own/pull this junk don't care, and you can't tell them any differently without them getting defensive. Had one last week, he loads his tractor and the tongue flips up off of the ball, takes out the back glass of an escalade as well as the rear door. Blames it on me for not checking it (and I had nothing to do with it other than driving the tractor TO the trailer-but not onto it). I check his setup. 1 7/8" ball, 2 5/16" coupler. I advised him of the situation and he argued saying that he's pulled that trailer with that ball for over 25 years. So I took it as "you can't fix stupid", and therefore at that point I quit trying.