Those older trucks are just not up to pulling that kind of load. Back in the later 80's, 10,000 lbs was the approximate ceiling for 3/4 and 1 ton trucks. The reason is that the GCWR would still be over 20,000 lbs on the 1 tons, and they did not have the power to weight ratios to handle much more.
As you mentioned, get the right tires on the truck. Also get a boost and exhaust gas temperture gauges installed. The gauges will allow you to see if the truck is building enough power and the EGT will allow you to back off the throttle when you reach high temps. You could also contact Banks to see what the boost and EGT thresholds should be. Then load it up and compare the results.
I've owned a few GM 6.2L diesels (still have one) and with the banks turbo, max boost should be only about 7 psi and max EGT should be about 1100 to 1200 degrees. Turning up the fuel will get a bit more power but the temps will sky rocket. The GM 6.2 and the Ford 6.9/7.3 engines do not have coated pistons AFAIK, so EGTs cannot go above 1200 degrees without melting the pistion crowns. My guess is your numbers for the 7.3 will be pretty close to a Banks powered 6.2L engine.
Another thing to consider is that with 99K miles, the injection pump could be starting to wear out, giving less pop pressure and poor injection timing. A common issue with the GM 6.2 is timing chain stretch, so injection timing slowly backs down, resulting in less power and hard starts. GM injector are also known to wear out by 100K miles. Since the engines are similar in design, I would look at all these issues. A good Stanadyne authorized repair shop could rebuild your injection pump, calibrate it correctly and can refresh your injectors. It may be worth looking into if you intend on keeping your truck.
When you have the engine as strong as it can be, another thing to consider is a gear swap. Your could always swap to a lower ratio to give better towing performance. It will reduce top speed, but I assume that is not much of an issue.
