re: How early should I start planning my Tokyo Olympics trip?

Start keeping a look at flight price trends. This way you will know what the cheapest/average option is. And with that knowledge, book your flight as soon as you think it is at a reasonable price. No doubt flights will be much more expensive during olympics. But if you know what a good price is, when airlines open their booking ~330 days out, you will be able to jump on any good "deals."

Apart from that, not much else you can do so far out.