Load ranges D and E apply only to LT (light truck) rated tires. P rated (for passenger) apply to the tires that our trucks are equipped with out of the lot. P rated tires typically have lower weight ratings but are much quieter on the road and give a much smoother ride than light truck tires.
Many people feel that they need LT tires on the truck to make it a "real" truck. I think this is a waste of money, as any of the P rated tires will easily handle the load ratings the Tundra can carry. LT tires are more resistant to puncture due to the fact they have more metal in the tread, but they are stiff and noisy.
I have P rated tires on my truck and have overloaded the bed with unseasoned oak many times and never had a problem with the tires or any part of the suspension for that matter. I also carry a 600 lb plow on the front and push a lot of snow on these "inferior" P rated tires.
I recommend you save your money and improve the comfort of the ride by staying with P rated tires. LT tires are for the 3/4 and 1 ton trucks out there... let them have the bone jarring ride.