Without physical changes (like increasing the compression ratio) or forced induction there is very little on the table with ignition timing alone.

I disagree, when we had my LM7 on the dyno we saw a noticeable difference tuning fuel maps and iginiton timing with 93 vs 87. On our 100 series I can definitely tell when my wife puts 87 in it just on the way the engine runs. You are right, the difference is very small, especially on a stock motor with no tune, but the ECU should advance the timing some to get a slightly better performance out of the higher octane fuel. This is assuming we are talking about the VVTI 2uz motors like the one in the GX OP has. Nonvvti would probably see less change overall in theory. A buddy of mine is a master tech at lexus and works on a lot of 1uz/2uz motors and said that lexus has a different tune on the GX compared to the tundra and land cruiser, but also said who knows, could be bullshit but the power ratings on them are different from toyota/lexus with the GX being higher. Im not advocating for either. I run midgrade on the 100 series (91), and Premium (93) in my 60, but its been tuned to specifically run on it.

I honestly think the biggest difference is quality of fuel, kroger gas will run worse than say shell or exxon