There's some availability on LAX-ICN. "Price Calendar" view tends to be more useful if you have more availability. LAX-TPE looks to be more of a challenge finding CI flights with availability. Note that these routes won't qualify for Amex 15% award discount since they are not DL metal (LAX-SEA-TPE qualifies when flown on 100% DL metal). D1 awards are available on LAX-SEA-TPE for 110.5K one-way for flights through the end of April (award fare rules do not permit them to be booked beyond this date).
The following are one-way, non-stop Economy awards.
These are D1 awards with 110.5K awards on LAX-SEA-TPE route with Amex 15% discount applied.