Hi Ben, and welcome,
I'm a fan of the U-1300L with camper.
A PTO generator works fine, if you need that much power. I use a 10kW PTO generator (on another Unimog) for emergency use and it works fine, but, consider the fuel usage of a big engine like an OM-352 or OM-366 (both found in U-1300's) running at speed to get that generator on frequency. Plan on several gallons of fuel per hour, and that adds up. Also, a Diesel engine does not like to run with low load for many hours. A smaller generator, Diesel powered, rated at near the load you require, would be much more efficient and won't wear out your truck engine.
You might not find a U-1300 with a PTO, either. If the truck has an overdrive then it won't have a PTO.
Few military U-1300's have overdrive or fast axle ratios. However, many of the ex-fire service U-1300's do have fast ratios (like 5.3:1), and a Claas overdrive can be added (cost approaching $10k now, if you can find one). In addition, the fire service trucks often have a torsion isolating bed needed for a cabin build. Don't want that box twisting on the road.
Towing a reasonable load is certainly doable, but expect slower speeds. I pull an M-105A2 trailer with my U-1300 and know it's there, and I don't put "3-4000 lbs" in it.
The engines in these trucks are not overly powerful, just sufficient, and efficient. As the load goes up, the speed goes down, and gear shifting is needed.
Another point about the SBU series of Mogs: These were the last of the mechanically injected engines with no computers or electronics. To me, that's a huge selling point.
U-1300L Unimog with 10' Alaskan camper, OM-366A turbo-Diesel, fast axles, overdrive, Werner 12k winch
Various other mogs for work and play.