In my experience, early C availability is not great, especially if you want to travel only on certain dates. If you are retired and don't care when you will travel, then it gets better. If you are willing to book economy and take a chance on clearing a waitlisted C, it gets better.

I think that AS award availability to Asia is probably better than AA C availability to Asia.

I would probably peruse AS award threads on the carrier you want to book. I'm going to guess it will be JL and not CX but I could be wrong.