MargaretB... you are right on the edge of benefitting from a 3/4 ton.
It isn't just the 6,000 lbs of trailer and the 780 lbs of tongue weight... it is the 22' x 8' x 8' sail that you will be dragging through buffeting winds from all directions. 60 square feet of Frontal Area is a huge drain on towing capacity, and yet it is rarely considered until the anemic tow vehicle is upgraded. Ford used to mention Frontal Area in their towing guides in years past, but I'm not sure what they do today.
I have several bumper pull trailers... a 16', a 20', and a 24'... all enclosed. I have some experience with actual tongue weights of these trailers, loaded and unloaded. Based on this experience, I HIGHLY recommend that you MEASURE tongue weight with a scale... do not rely on any type of rule of thumb percentage based estimation, such as 11% or 12% etc. Those figures are fiction, compared to ACTUAL tongue weights I have measured... which surprised me.
For example, remembering back to when I first received my Sherline tongue weight scale about 10 years ago, I had ball park estimated the tongue weight on my loaded 16' trailer to be 800 lbs. It turned out to be almost 1,300 lbs. Weight cannot be seen, nor should it be estimated. The best practice is to MEASURE your tongue weight, and then choose your hitch rating and spring bars for your weight distribution system accordingly.
You listed a bunch of trucks in an earlier post. My favorite pick of the ones you listed is the 2014 GM truck with the 5.3L. Apart from towing, that truck will ride and drive empty like a dream. That truck is quieter than my electric hybrid car! The 2014 5.3L has all the technologies to save fuel... variable timing, cylinders shutting off, etc. However, you might be on the edge of it's capacity if your trailer weight drifts higher than 7,000 lbs.
You mentioned truck brands, and engine displacement sizes. That's good info to help people here help you choose. But there is one more important data point that you should add to your spreadsheet of considerations: Rear Axle Ratio. The same truck with the same engine will perform quite differently if fitted with a 4.10 rear axle ratio, versus a 3.42 axle ratio. The higher the number, the lower (deeper) the gearing.
The deeper the gearing, the more towing power you will have, which will effect your entrance into freeways when getting up to speed to safely merge with traffic. It will also effect the number of gears that are useable to you in your transmission when pulling up a grade. If you have too tall of a rear axle ratio, such as a 3.42, you will have to downshift your transmission sooner than you would with a deeper rear ratio like a 3.73 or a 4.10. This effectively gives you more useable gears on the grade, which lowers engine rpm and in cabin noise level through your pull, since you won't have to downshift to 2nd as early as you would with a taller gear.
Keep looking. For a budget between 21K and 31K, I'd like to believe there are options out there that would afford you a larger margin of safety when towing. That being said, if you only plan on towing 10% of the time with the truck, and the other 90% of use is as a daily driver while empty, then you might want to stick with the 150/1500 size... but get deep gears, know your actual tongue and trailer weights, and see if the truck's towing specs will match your application.