Based on my experience, and what the Calif Highway Patrol recommends, I would never run P rated tires on a tow vehicle. They would always be LT tires 8 ply or greater, E rated. Speed rating doesn't matter, because you're not racing anyway. Door sticker is by vehicle mfg, based on the tire size they install at the factory. If your tires are same size, and your vehicle is not towing, those are valid. If you fit larger tires, it's ok to be 5-10 psi lower than door sticker IF YOUR TRUCK IS UNLOADED AN NOT TOWING.
Once you add a load or hitch a trailer, the door sticker goes out the window. I always inflate(d) my truck tires within 5 psi of max on the sidewall when towing or carrying a load. Whatever pressure you choose, all tires should be within 1-2 psi of each other, if they are on the same axle.
With under-rated tires, or with too low of a tire pressure, or too flexible of a sidewall, a heavy load over-stresses and therefore over-heats your tires. Even just pulling a heavy load that isn't on the axle can overheat the rear tires because of the torque of the drive axle. Blowouts while pulling a trailer are just way too dangerous for you and for everyone else near you on the highway. And hot tires cause blowouts.
How do I define a heavy load??? Is it more than half of your towing capacity the manufacturer designed into your vehicle? Then it's a heavy load. Especially with amateurs like us at the wheel.
2006 Jayco Seneca 34SS
2006 Jeep Wrangler Unlimited Rubicon Toad