Nowadays you usually don't see much premium cabin availability at saver rates until the last week or two before departure. With credit card points, the best option tends to be Aeroplan for NH or UA, and United for AC. Both United and Air Canada mark up their own flights in their own mileage programs, kind of counter-intuitively. Using AA miles for JL is often an even better deal.

My suggestion, if you want to actually make plans in advance, is to start by securing economy seats through AA. AA metal HND-LAX is 28k one way in economy, 45k one way in premium economy. JL economy can be had for 35k. There is plenty of availability, cancellation is free, and you get the miles back immediately.

Then keep eyes peeled for better options starting a few weeks out. I would focus on searching through United, Air Canada, and American. UA and AC usually show the same flights at saver rates, but United is cheaper for Air Canada flights and Air Canada is cheaper for United flights. Getting JL flights through AA is still doable but availability is iffy. You can luck out and find last-minute F but it's really a crap shoot as to whether it will show up.