Your sticker is giving GVWR, not GCWR. GVWR is the max weight allowed on just the truck. GCWR is the max allowed combined.
If you have an auto the 2240# would be about right--and that assumes an empty truck.
An 18' open utility trailer made of steel angle weighs 1,600# empty. An enclosed 18' utility trailer weighs 2,000# empty.
A 4' wide, 6' long Wellscargo enclosed mini wagon weighs 600# empty and has a 2,200# axle.
If you are going to follow the Ford towing guide, that might be doable. But if you have just yourself and a truck filled with 600# of you personal effects even that isn't going to fall under the guide.
It's going to be impossible to tow something substantial and meet the guidelines. I would probably set a limit of 3,000# total trailer weight. The frontal area is much more important than the weight. If you make sure you aren't using more than 1/4 throttle on hills--that means downshifting and being humble, you will keep the heat under control.
This trailer was 6'8" wide, 16' long (13' box length--cargo trailers give the box length travel trailers give the over-all) and 7'8" high. It weighed about 3,000# when loaded for camping. I pulled it everywhere with that little pickup, which was a 2.6 liter auto. It went from 26mpg at 65mph to 19mpg at 60mph. Going up hills required downshifting to keep that light throttle touch, and accelerating wasn't spectacular but I would have hauled it cross country.
Later, I used my 4.0 Ranger and it woud hold the cruise on any hill with it. You can definately see that you
could hurt a 4-cylinder by trying to keep up with traffic and that's why they recommend against. The 4-cylinder has the power, but you would spend a lot of time with the pedal to the carpet. But if you replace the cubic inches with cubic gray matter you can get by.