The new Ford transmissions have a thermostat. They're designed to run very hot. Much hotter than in the past.
Make sure you lock out your overdrive gears and let the engine sing in the hills. I towed completely across my state a week ago at 3000rpm with my 6.2. Only letting it up shift for perfectly flat grades.
The Super Duty is more capable off road. More flex. Locker ready front axle. Strong axles. The Dana60 front axle is so perfect'y suited for an autolocker, that it's offensive to me NOT to add a front locker ASAP. The SD's weak spot is it's weight in soft, slick, deep mud. You'll need Cooper STT tires on one, to keep up with an F150 on decent AT's. Expect to run 35" tires for the same under axle clearance as a 150 on 33's.
As you're aware, stock Ford shocks should be replaced before your first oil change. Par for normal GM, dodges, etc.etc.
35x12.5r18 on a 18x9 +18 wheel fit stock.
It'll have a rougher ride no matter what. But that's all in your head. Foam seats half a foot thick aren't exactly going to draw blood on a bumpy road or anything. BDS 4" suspension, and Accutune or Filthy Motorsports King or Fox 2.5 shocks helps a ton. 37" tires will fit a 4" lift easy. Any wheel bigger than 18" is going to noticeably degrade ride quality.
Also note that the new SD's are lowered thank to lame 5'er owners. They aren't as tall as '17-18 SD's.
The SD won't even know that trailer is there. Way more confidence in all road conditions than an F150. That trailer maxes out a 150, but is at the minimum of the SD's specs. The most it'll do to an SD, is smooth out the trucks ride.
If you can get another year out of the 150, consider the new 7.3l gas engine coming out. The 6.2l gas engine is overkill for your trailer. I'm afraid the diesel might be too much engine. The diesel is another 1000 pounds of weight, which hurts even more in soft mud. And the extra cost of the diesel, covers more than an entire longblock 6.2 engine dealer replacement ($8000). Major repairs can go north of $10 000 with the diesel easy. Make sure you need it, and make sure you do enough hwy miles to clean it out.
My 250 never commutes. It's a weekend warrior, that only gets pizza on weekdays. I live in the snow belt, where a diesel wouldn't even reach operating temp, more than once a moth in the winter. Basically, I'd ruin a diesel, and go broke keeping one running.
I'd consider an Xl, XLT, STX, with the Tremor package to get the front lsd. Instead of a Lariat. Avoid the adaptive steering, and moonroof. Avoid drive through car washes, and/or at least grease the ''plug of death''.