P series tires on a Tundra

I was recently in the market for new tires. I was running P275/60R20. The guy at the tire store ask if I haul or tow. I said yes...both. Then he tells me the P rated tires are barely rated for the weight of the truck and I should be replacing them with LT series tires with a higher load rating. This ticked me off to know the last tire store sold me P rated tires if this is true. The sticker on the driver’s door jam even says it should have the P rated tires so I’ve never thought anything about it. What’s the opinion of the site’s Tundra owners? Should I go with the LT series?

 

The p rated Falken's I had were bad... Bouncy and didn't last, especially compared to the E rated Coopers I replaced them with.