Did you drive on the beach with a previous vehicle?
I am assuming you are airing your tires down when you get to the sand (if not then I would agree you are going to need something bigger than stock and you can skip reading the rest of this post). I've driven on the beaches here on Long Island with a 2-door Blazer with 31x10.5 tires, and a Crew cab Dakota with stock tires. I did not notice a significant advantage with the larger tire size. But I cannot say with certainty that the stock tire on the Tundra is fine, because I have not tried the beach with a Tundra.
However, it may rest your nerves a little to know one of the last times I was out, this family next to me took their Sequoia (I think it was an 05) and that had stock 18 inch rims/tires. And that did fine.
I only go about 4 or 5 times a season, but I've only seen 2 people get into trouble since I've been going. A f-150 got stuck because he got too close to the surf, and the other was a subura baja which the problem was more the lack of clearance than the lack of traction. And by me, most people are driving stock vehicles. I am guessing because the audience the beach draws is throwing their disposable money into the water as opposed to into their vehicle
So if it were me, I'd save the cash on new tires and gamble a little....I'd hit the beach on a busy day. Try to give it a test without going too far in. Worst case, you get stuck and you need to ask a fellow fisherman to help get you out.