go to to 4:10 gears? 34" inch tires? what? none of that makes any damn sense, my 15 Silverado CC with 33" tires, a 325 and 3:70 gears, Pedal Commander and AFM disabled lights em up all day long driving around, i can barely drive it in the rain in 2wd (i use 4wd auto) because it spins the tires too much trying to pull out into traffic. i have a 2004 Sierra shorty with 6" lift and 35" tires and 3:70 gears and a 325 and it does pretty much the same thing as well with factory rated 300hp, i can get that thing sideways in a half a second, so a 420hp/460ftlb truck, with 3:70 gears, and 34" tires should shred tires all day long without breaking a sweat, and that combo can handle even more tire than that. thats 30 years plus driving 4x4 trucks and off roading talking
" There's at least a 1-2 second delay when flooring it and while the truck runs out strong it just doesn't have the responsiveness" is to me the key here, does your tuner have a pedal/throttle adjustment? i cannot say enough about my
Pedal Commander, its a game changer, basically instant throttle response over the lazy factory setting. if your tuner doesnt support that get a Pedal Commander.
also one simple thing to check is the gas pedal flex issue, i believe some people call it the "paint stick fix", i have seen this issue first hand on several friends trucks, mine has adjustable pedals and had no play/flex at all, but the issue is the gas pedal has play or flex in the mounting plate that prevents the throttle from activating fully without a delay first, people have "fixed" it using a piece of a paint stick under the pedal mount assembly area,
these 2 items alone could very easily account for a huge part of your issue, the pedal flex and the factory pedal response lag is a major contributor to what you describe, you are giving it throttle but its slow to respond,