So, I ran an the old MTR in 285/70r17 that was D rated in death valley, rubicon, moab, tellico, and a ton of highway to get to all these trails and then the current KM2 285/75r17 which is E rated on the same stuff.
Normal driving with E rated is rougher than D rated (obviously) but in a rattling sort of way. I feel like I wanted to run lower psi more often with the E rated when on long corrugated trails over the D rated which I was pretty happy at about 25 psi to soak up dang near everything.
Now when I am loaded to the brim with the ability to overland for about 6-8 days between needing fuel, E rated starts to get squished a little more, and feels more compliant.
Now with the Tundra of yours, you will probably not notice the firmness of an E rated as much as me, my buddy's tundra has E rated KOs and they feel very planted, but not overly firm on gravel roads.
As far as width, .45 inches is the difference between a 285 and the 10.5. I get it, I think the 34x10.5 is an almost perfect tire for toyotas and jeeps that want to doing everything relatively good. It's tall, it's stock width, it's D rated to keep weight down (86.5 lbs on BBS 17x8 rim), triple peak rated, with a sidewall that the titanic wishes it had, which is why I took the chance and bought one to test. But the KO2 34 definitely does not look nearly as pizza cutterish (yea it's a word now) as the KM2 255/80r17.
I honestly thing the size for you should come down to the suspension you have and the terrain and speed you want to do the best at. I have a tall truck, and could fit a 36 easy on gravel roads, but up travel is whats going to get you. If you already have a 35 that fits good, then run a 35, if you are looking try to get to a 35, I'd suggest the 34.
Hope I didn't ramble too much, been build custom cars and 4x4s for years, and I have to really think about what's pertinent and what is just unnecessary.