Jes, mr. Soekarno Hatta is right. You cannot cross the Pacific twice on your RTW, otherwise it wouldn't be much of a RTW, would it?

So when returning to BKK at the end of step 2, you'll have to route through Europe. The fastest routing is probably YOW-YYZ-FRA-BKK using AC, LH and/or TG. Of course, given that there still are miles remaining, you could fly via US, or take a few sidetrips in Europe or whatever.