I would suggest the first thing to change/add would be external coolers, specifically transmission cooler.
With the 6 spd, gears are not really the problem and should be the last item. Even with 3.08 axle gears, the 6spd 4.03 1st gives you a lower final low of 12.4 vs the old 4spd with the 2.45 1st with even 4.1 axle gears would only be 10.05! The 6spd also has a nice spread to keep you in the power band, you will likely end up in 4th, which is a slight underdrive making it like towing in direct with a 3.54 axle.
As you can see, the gears are not what makes the difference between 5100lbs and 8100lbs, it's the coolers. So start with a transmission cooler and go from there.
You want to add a stacked plate cooler, and DO NOT bypass the "tiny trans cooler" inside the radiator. That liquid to liquid heat exchanger is FAR more efficent than even the best oil to air stacked plate cooler, especially in situations when we often find ourselves towing, under load going slow up a hill, or trying to push the trailer back up a hill into a space. In these situations there is not a lot of air blowing over the stacked plate cooler and it doesn't do much, most of the cooling is being done by the oil/water heat exchanger. Ford made the mistake of not listening to their engineers and deleted the radiator cooler on some of their trucks at one time, and even newer vehicles like my 04 explorer. The result was as expected, hard slow pulls and backing into uphill spots resulted in quickly overheated transmission fluid.
You are not as bad off as it may seem, a aux trans cooler and aux oil cooler are not really that expensive, and if you decide later that you really need the gears, 2WD is under 1k. Your real limitation on a 1500 will always be payload. If you look for trailers with a dry weight around 5500, the numbers when loaded: weight, tongue weight and length pretty much work themselves out. This seems to be the sweet spot for standard 1500 class vehicles. You can go heavier, but then it really becomes a ballancing game.
Good luck to you!