My name is pteck, and I have a problem. I have an unjustifiable like for all things tires. Whether A/T, max summer tires, whatever.
To the OP, you understanding is correct. With each parameter and tweak, they all tend to lean the tire towards certain qualities. More sidewall generally means more flex. From P, XL, to LT, will go up in sidewall stiffness, load, and durability, yet less comfort. To an extent, the compliance can be adjusted with air pressure. So more pressure when under tow will help with added stability.
Also worth some thought is whether you want to go up in overall tire diameter too much. More diameter reduces gearing, but more importantly it will also reduce brake torque. You're not going to a 35" tire so it's just for your awareness.
A 20" wheel will certainly aid lateral stability. An LT tire, will again increase that stability. To answer your question, between your two choices, you can't really go too wrong. It's a personal and aesthetic choice at that point.
I have a Land Cruiser in Lexus guise (LX570), that generally uses the same wheel and tire sizes the Tundra uses. Not recommending you go as far as I have, but I have 20" wheels with 33.2" LT tires, size 305/55/20. Tows beautifully. Yet the premium suspension and NVH isolation of the Lexus keeps the AT tires so well behaved that you would never know they were aggressive off-road truck tires.