Where to find the cheapest Business class tickets from South Korea to LA?

If you are finding $3600 into LAX in First Class, that is a really good price honestly. First Class tickets aren't going to be discounted, or will you be able to find it much less on other websites. There is a discounted First Class fare, however you have to know what to look for. Try looking at some of the various websites for codeshare partners. You may find that Delta would sell a code share flight on Korean Airlines cheaper, and visa versa for any other partnered airlines. Right now American Airlines is running amazing deals to Asia, so you may want to check that.

As far as booking a one way, you need to consider the fact that tickets are sold based on round trip, so you may find that a one way is even more expensive than a round trip. Also, if you have US Citizenship, it shouldn't be a problem, but there are entry requirements for coming and going from the US and usually you must have a round trip ticket purchased. One way International tickets normally get your flagged for full searches at Security and have you detained in Customs and Immigration longer than you would if you were to purchase a round trip ticket.