The door sticker is the rating based on the stock tire. Given tire manufacturing changes through out the life time of the truck, the sticker can be wrong. Changes in formulas, compounds etc, manufactures can make better tires. ...Ok enough with my BS....
Go by what is on the tire, not the door sticker. Next, when reading the recommended PSI, this is for the MAX weight load capacity the tire is designed to carry. If you are not planning to use the tire at its max load capacity, you can lower the PSI. As what Brian and Nick stated, you may want to drive a bit through some water and see what the contact patch is looking like. You want a nice even surface though out. Too much air and as Brian and I have experienced, the outsides will cup.
So you will have to play around to see what the front and rear tires are happy with. IMO, I try not to go more than 5-10PSI lower in the back than what is in the front.