Hello!

What class are you planning to travel in? Getting seats on TG will generally be the easiest, but that does mean BKK so perhaps think about that one just as a back up. OZ via Seoul is a good option, but ICN is a long (almost 2 hour) trip from central Seoul so if you are planning just a stopover, bear that in mind too. J class is not a flat bed however.

Air NZ is supposed to be great but not flown them before, but at least you can do a round the world, and with more connections from LAX or YVR is using AC you can get to South America too.

Once I know the class I can offer a bit more help, I've just booked some seats from London to Melbourne and back from Sydney.