Oh. I gather you have already transferred these to AS? If you had transferred to Korean you would find that KE has pretty good availability through their own program. Partners like Alaska only get a few award seats. Korean keeps the majority of awards seats for their own members and their availability is pretty good through their own SkyPass program. Their rates are a bit higher than Alaska though.

There is a whole thread here on CX (Cathay Pacific) award availability here. You should check it out. CX does not show award availability on the AS website, you will have to call to check CX award availability with AS and to book but it is better to check availability on other sites first then call AS to book. Qantas has a good award search and shows CX availability.

Another alternative I might suggest is to fly Japan Airlines (JAL/JL). Their lie flat biz product is said to be excellent and their First is even better. It's 65K miles one-way US to BKK and you can find dates if you look a bit. Note that JL flies through Tokyo and they operate out of both airports there, Narita and Haneda. You might find very few dates direct through one airport but if you are willing to do an airport transfer NRT-HND more options open up. Alaska has an almost unique feature of their program where you can get a stopover on a one-way ticket so you could book something like JFK-NRT stop in Tokyo for a day or two or more, then continue from either NRT or HND to BKK after enjoying Tokyo and while giving yourself more options for award availability from Tokyo to BKK (you can take any flight with availability even if you have to stop in Tokyo for a few days).

I see through availability on JL in Business Class on 7/31 JFK-NRT-BKK for an example of what is possible on JAL.

Using CX and JL as two options I think you should be able to find something, possibly with CX one way and JL the other.

ETA:
It looks like CX has pretty good Business availability. I think CX might work best for you coming from the East Coast. JL is pretty good from the West. Use the Qantas site to search for CX availability (from the CX gateway cities in the US).