OP first good for you for weighing and knowing your axle weights and for useing a WDH. This is where safety starts. Many here try to short cut it by just getting a bigger truck which often just masks the problem.
Mitch had a good point; that a payload number means nothing safety is about axle loads and distribution and that if you are at/over axle and the axle rating on the new truck doesn't change.. I suspect you didn't list your front axle weight because you haven't got it dialed in yet. At any rate your rear axle is ok assuming you still have the pre hitch weight on the front axle. So if you add any weight you will want to make sure it gets transferred to the front axle or you will want a bigger truck.
You say the gearing on your truck now is nearly perfect. First gear now 14.80 with the 3.15 axle 10 speed 14.77. No issue with that and its normally not the most important place to look. If it has the power and speed (gearing) that you want to cruise at then you don't want to lose that. Now you have 4.05 in 4th and 3.05 in 5th or first overdrive. This is likely where you spend your time. It a lines well to the 10 speed 6th & 7th at 4.00 & 3.15 respectively. The 3.15 should move that load as well or better from a stop and at your cruise speed.
On another note sounds like Ford is going to offer the 3.0 turbo diesel in the F150. It won't be as fast but it will move the same load on about half the fuel. Just depends on what is important to you speed or preservation of your capital.