IMO, a 7.3 w/ a 4-spd auto and 235 hp isn't going to provide much of a performance upgrade over your current 5.7/6 spd. I've driven a 2000 7.3 towing about 10k of gravel, and I was honestly far from impressed. Keep in mind that the 4 spd auto behind the 7.3 isn't known for its durability, either.
The mid-2000's Duramax will have a 5 or 6 spd transmission, with a good power advantage over the 7.3. Combined w/ the great Allison transmission, power, and good history for reliability, the Duramax is the diesel powertrain I'd prefer from the early and mid-2000's. The 5.9 Cummins only has a 4 spd auto, but also has a good power advantage over the 7.3. Regardless of the badge on the front, the Duramax and Cummins will provide a noticeable improvement over what you've got.
One final note -- an F150 Ecoboost w/ the HD Payload should have enough capacity to tow your trailer well, and the twin-turbo engine won't lose power at elevation. The payload ratings and towing ratings are going to match up pretty well with an early 2000's 3/4 ton. Honestly, with the trailer you've got, that would be on my list.