before the slave cylinder crapped out and the Dex-Cool ate the gaskets, we pulled over 10K all the time with dad's 98 GMC C3500 5.7L Vortec NV4500 5spd 2wd with 4.10s. Some of the best loads were well north of 20,000 lbs combination, I dont think we ever broke 30,000 though.
The 350 is not going to be your limit, its the gearing and the chassis and brakes.
Keep in mind they put the 350 in old C series grain trucks (C60, etc) and guys would stretch them and put a tag axle and a 20 foot bed and would gross 50,000 lbs with them hauling grain. but they had deep geared trannys and rear ends and never set any speed records doing it.
Also, towing over weight is a personal responsibility. Drive safe and leave plenty of following distance, and be prepared to take the ditch. Cross fingers and thank the Lord I have never had any issues towing overweight. being legal weight can only go so far to battle stupidity. Occasionally you see someone at perfectly legal weights do something stupid and wreck the truck and possibly injure others.
I would say find a factory heavy truck to tow (2500HD, 3500 SRW and 3500DRW), and yes one with a 350 will be just fine. You cant "make" a 1 ton from a lighter truck, there is so many different things people overlook when doing their half-ass swaps.
If you want low cost decent pulling ability and fuel economy, look into a 6.5L diesel. a full set of injectors for one costs what one does on a D-max. With a good maintenance program and understanding, they are good tow rigs.
With some neglect and refusal to learn anything about one and blindly throwing money at one and letting your favorite local idiots work on it, it will be the most miserable POS you will ever own.