SQ flies NRT-LAX and sells a one way ticket for around USD 800, IIRC. Also, during the C Johnson debacle, I noticed that AC has reasonable one ways to Vancouver.

But I really don't see that buying separate tickets is going to be a better option than a Star RTW. There is a Star Lite option for economy. Now, buying them from the US has always been the highest price. Actually, from Japan is among the cheapest in business despite the strong yen. Around USD 8,000. I bought one last fall and managed to squeeze in a RT to NZ, which would cost USD 3,000 round trip in peak season in economy.

So if you plan a RTW well then you can add in additional side trips.