The hard part is finding awards within Asia.

If you are willing to book last minute and are fairly flexible, you should be able to find business or first class award space on JL as far as Tokyo (and back). This can be booked on AA or any OW carrier that you can transfer miles to. If you have AA miles, it will be 60k miles each way. If not, but you have CC points, transferring to BA is probably a good option.

From there you may be able to buy a business class round trip to TPE for a little under $1000, or economy for $400, or $250 if you are willing to fly an Asian ULCC (Peach Aviation? TigerAir Taiwan? Scoot?)