I would say the issue is the springs, not the tires. Being over on the springs is not as bad as being over on the tire from my experience. I would toy with adding a leaf to the spring pack, air bags, or completly redoing the spring pack would be my first thought and preference. BUT< that is also the how I use my truck, better to have springs generally speaking than air bags. For some that carry truck campers, air bags would be a better option.
For the OP....not sure I would worry about it, since he has a 350, the issue of the overheating RA as mentioned by one that had a 1500, is probably not going to happen.
Enjoy the truck, make sure you have a paid for tag that is greater than what you are grossing at, as that will be the issue you will have if pulled over, more than being over the manufacturs ratings. At least that has been the case for me here in Wa st.
Marty