For HAN-BKK (and most any other legs in South-East Asia), you can save a fair bit by flying low-cost carriers like Air Asia. In fact, I'd go so far as to suggest that you should just get a cheap return fare from Fukuoka to Bangkok, Hong Kong or Taipei, and plan the rest of your trip using low-cost carriers. Eg. Air Asia, Jetstar and Tiger all fly between SEA and Australia, and from there you can hop onward to NZ with Pacific Blue etc.

A starting point: http://wikitravel.org/en/Discount_carriers_in_Asia