That explains a lot. For towing that load with a stock 2003 tranny, a maximum of 40-50 HP, and about 120 ft/lb torque is about it before it'll start to slip. If you want more than that, you'll have to upgrade the tranny. A couple tranny builders can upgrade it to handle just about any level of power, limited by your willingness to spend. If you like your truck, want to keep it, and want to run with the extra power, a tranny upgrade may be a better option than a new (new to you) truck.

80 HP and 150+ torque will do exactly what you're seeing. You need less power, less load, or more powertrain. Simple as that.

Also keep in mind, extra power often means higher EGT's, which can mean a tranny that survives, but an engine that doesn't. If you don't have gages, with at least a pyrometer, you'll never see the damage coming, and have no way to know when to ease off. These engines are tough, about as tough as any in history, but they have limits. Stay within the limits and they'll live indefinitely. Exceed the limits, and it's only a matter of time before you find the limits.