Asian award availability has been very tough to find. It'll be extremely difficult to find it on short notice at one of the busiest time of the year. If you're willing to wait until the last moment, you may get lucky and find something that pops up. You may want to try and use an award service that looks for award space on a daily basis or consider flying coach.

You may also consider flying somewhere else in Asia and paying for a shorthaul ticket from there to Taiwan.