The places the OP wants to go and timing suggest a RTW. Perhaps look into starting from BKK for a cheaper fare (SIN-BKK is cheap extra ticket).

Itin could look something like BKK-SIN-FRA-NYC-RDU-ORD-HNL-NRT-SIN-BKK which fits under 26k miles and so use the cheapest *A RTW, Star Lite.