I did similar calculations when we upgraded to our current Regal 2400. I was within the limits of capacity for our F-150 however not by much, verified weights at a CAT scale. Even though the towed weight was below the trucks capacity I definitely knew the boat was behind me and made traveling very tiresome. We now tow with a 3/4 ton diesel truck and I hardly realize the boat is there and arrive at my destination much more refreshed. The point of this is to say make sure you have some cushion and are not at your max. capacity as the trailering portion will not be enjoyable.
I towed at 2k lbs over the factory limit for 10 years with my '99 Durango (with some simple and effective modifications to make it feasible and safe). I I have no regrets as it worked very well and proved to be a very economical decision at the time, plus my kids were still young and we really made good use of the seating for 7. When the Durango finally rusted out and needed to be replaced, like you, I went with a 3/4 ton diesel (bought used with 180k miles and no rust for very little money). Also like you, I find trailer towing much more enjoyable now (it actually went from being work to being fun). It has also really expanded my boating destinations since I don't have any qualms about going anywhere with it. 2018 will be my fourth season with it and I already have some big trips planned.
Anyway, in case anyone cares, if you want to dramatically increase the tow capacity (obviously not "officially", I'm just referring to physics and engineering here) of any vehicle, there's a very simple modification you can make: Put tires on it that are the same width as stock but have a smaller aspect ratio (assuming same wheel size here) and a softer compound than stock. The low profile tires not only make it easier on the drive train by lowering the effective final drive ratio, they also lower the tow vehicle's center of gravity, increase the the power of the brakes, increase traction, and dramatically improve handling. For even more safety, you can also install higher performance brakes (including brake fluid) and shocks, and if you have adjustable front suspension pre-load (pretty much any truck or SUV with torsion bars does) you can level the tow vehicle so that it sits right with the trailer attached.
Here's a pic of my leveled Durango with the low profile, and sticky tires that I ran in during towing season: https://www.facebook.com/photo.php?fbid=1030767061375&l=2d5bd2f661
I bought 5 extra wheels for it for cheap money on craigslist which made tire swapping very easy and since I ran the thing into the ground, the only real added expense was the used wheels because by swapping tires, I doubled the amount of time the tires lasted. I was also able to run studded Winter tires outside of boating season which was awesome and gave me peace of mind when my kids started driving.