Welcome to FT, cadogan1!
The cheapest options appear to be NW and UA, though you may have a better experience with one of the Asian carriers. I've never taken a trans-pac on NW, but if you take UA in Coach, I suggest a 777 over a 747. You should also look into round-the-world fares, as it may be cheaper and easier to do it all that way if you can meet the restrictions.