Your itinerary looks good. I see not much what you can improve considering that you need to find space.
SQ would be better on their non stops US-SIN, but you will not find availability with US miles.
NH and TG are good airlines.
You could try to route thru europe on LH, LX, SAS or Turkisk to BKK / SIN, but (unless you can find the new LX Business seats at least on some legs) that likely adds some flying time.