The important calculation that was ignored was the load capacity for the two rear tires. With a drive axle total load of 6900 lbs. that works out to 3450 lb. per tire. I would bet that your factory tires are rated at 3195@80 PSI and so you are most likely overloaded where it counts the most. Overloaded tires are going to have more sidewall flex and run hotter and are much more likely to fail catastrophically - i.e. a blowout.
The payload and other ratings are based on the truck as it leaves the factory. Any modifications done later by the dealer or the owner can increase or decrease the validity of that rated amount. This includes the choice or rims and tires and any suspension changes.
In your situation I would be looking to at a minimum buy Toyo or Nitto tires that are load rated at 3750 lbs. and it would not be a bad idea to think about going with 19.5 rims and tires if you plan to tow a trailer or add a generator or make other changes that add to the load on the rear wheels.
