Thanks Fasternfaster. Yes, 305/55/20 can be done! No rubbing at all after the nip and tuck here and there. Refer to the links posted by Fasternfaster above.
I originally was planning on 295/55/20s. They would most definitely be an easier fit. Though there's not many tires offered in that size. In the end, I went 305s for a few reasons. The big 20"ers sit pretty flush against the sidewalls with 285s. I wanted the wheels inset as much as possible so they're not as exposed. I wanted more sidewall, and the only way to do that with a given wheel size is more diameter. And heck, my LX470 had 305s on 18s. My opinion, but I prefer the hunkered down look of meaty tires.
My stock LX570 wheels are 20x8.5 +60. So seems those TRDs are similar in dimension. You'll need 1" spacers in front for sure, but preferably all around to keep the track the same. The LX doesn't have KDSS to worry about, but I imagine a 1" spacer will keep these tires off the KDSS mechanism as well.
Really loving the setup. As much as I love fat donuts on small wheels, this setup is better for the 99% street driving I do. Steering is still very accurate and precise, with lots of cornering grip. Yet now I've got some real A/Ts in load E that I don't have to give a second thought to about punctures and road conditions. I know you're asking more about size, but I'd highly recommend you look into Falken A/T3Ws. Aggressive tire with great manners.
Bonus - 305/55/20 will even fit as a spare with minor tweaks.
Don't have many pics yet but here are a couple:
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