When I leave Japan to return to the US, I'm going to have about 2 months "notice" . Today, I was playing with this using Expedia(horrible), Kayak(ok), and Orbitz(lowest fares). They actually showed China Airlines($640) and Korea Airlines($920) to give the lowest overall cost, though I'd have to suffer through connecting flights. 

Usually you can get a better rate through travel agencies out in town. Ticket prices are usually best between 1 - 2 months before your travel date. If you look too early, you're going to pay a higher rate....if you look too late, you're going to find all the "published" teaser rates are no longer available. Travel in the fall is usually pretty cheap to LA.

I use cheapoair.com thier prices seem to be pretty low.
definitly check with the off base agencies like Yoko[girl suggested. They do get some great rates.

An online or offline travel agent can't do much for you here, especially with a one way fare. My subscription to Expertflyer just expired so I can't look up published fares for you. This site gives you the same information as a travel agent.

Actually one free site that is quite good for fare information is matrix.itasoftware.com.

Some FF programs like United offer one way awards now so you could use miles to pay for your one way ticket.

www.travelocity.com seems to work well for me, some non US flag carriers are great like ANA, JAL, Lufthansa, Air Italia and others have dangerous maintenance practices.

I didn't care too much for KAL as they were smoking in the bathrooms after disabling the detectors by placing a paper cup over the sensor and yes the cabin crew knew about it and tolerated it.

My trip is a long ways out, but I'm planning ahead. I do understand that timing is as important as the carrier when it comes to pricing, so I'll monitor fares for a while to see how they fluctuate.

Also, are there any "dead times" for Tokyo to LAX travel? Usually prices are lower during these times.

"Dead time" doesn't matter for a one way fare. For example, United and ANA will only sell a full fare Y ticket for $4,500 one way even if the flight is empty. This is an insane price for economy class. You can buy a one way ticket in business class on Singapore for $3000, which is also non-stop NRT-LAX.

On the other hand, Singapore has an economy ticket for 64,350 yen (incl tax and fuel surcharge) that is available on most days. It books into E booking class, which is pretty high on the economy class scale. You can change the date of departure and refundable with a 10k yen penalty. And you can credit this to United for full mileage earnings.

There are two factors that affect the price on a given day. One is that they offer a given fare, which can be affected by advance purchase restrictions but you probably won't have any for a one way. The second is the availability of the fare based on how booked the flight is on a given day. In this case, E class on Singapore is far up the scale so economy has to be close to sold out before it becomes unavailable. It is very unlikely that it will drop because it is a published fare through March 2012.

In my vast experience of travelling, the Singapore ticket is a very good deal. You can easily book it on their website.