Let's get something out of the way. You can do this and set it up to be safe. The question of a pleasant towing experience is another matter. I have twice towed close to my limits with 2 different combos. It's doable, its safe, but it has limitations. Short trips and stay away from long steep grades. I would not consider, even for a minute, towing over rated capacity.
I don't care how many anecdotal posts you find on the Internet about how the Tundra is "underrated". Says who? Some guy you don't know from Adam? People who will tell you a close to capacity, or over capacity, setup "tows great" more than likely have never towed the same trailer with a healthy margin of capacity. I see posts every week where someone says they switched tow vehicles from a marginal one to one with reserve capacity, and they always rave about the differences in towing and comfort. Also, I see plenty of posts by former Tundra owners who did exactly what you are considering and traded up for a 3/4 ton truck.
While your setup can be safe, what if the worst happens? You are involved in an injury or death accident while towing, even if not your fault. If the greedy lawyers find out that you exceeded any published limitation, what do you think they'll do with that?
Regarding dry weight, that's a fictional number. That's not the weight you'll be towing when loaded. For planning check the GVWR of the trailer, estimate tongue weight based on 13% of that number. More than likely you'll be looking at a 900# hitch weight. Plus you have growing kids. They weigh more as they grow, and they want to bring more toys. Are you taking bikes? Anything else? All of it has to be counted. You'll be exceeding your payload by more than 200-300 lbs.
Honestly, it seems to me you have your mind made up, that you're just looking for justification. If you do this, I predict in 1-2 years, you'll be looking at bigger trucks. Pay now, or pay later.
Chuck D.
โAdventure is just bad planning.โ - Roald Amundsen
2013 Jayco X20E Hybrid
2016 Chevy Silverado Crew Cab Z71 LTZ2
2008 GMC Sierra SLE1 Crew Cab Z71 (traded)