Jan 5 - both 149 and 107 have L0. I think this may be due to the season and closeness to new year.
Seems that 93 MEL-LAX is also zero'd out in L, as is 25 BNE-LAX (via AKL). Doesn't look like they want you to fly to LAX that day ;-)
The only other option you may have (if that date is not flexible) is to fly CX SYD-HKG-LAX - there have been posts about whether this is a permissible transit through Asia on a xONEx......
Only other option is to wait and see whether the waitlist clears