What class are you looking for?
AONE3 CX A Round-Trip 8231.00 (USD)
DONE3 CX D Round-Trip 5728.00 (USD)
LONE3 CX L Round-Trip 2557.00 (USD)
As for the return from LAS you might want to take CX or JL instead of AA. If you aren't flying coach avoid the EG flight between NRT and TPE, take NRT-HKG-TPE or HKG-TPE.
So you could do LAS-LAX-HKG-TPE or LAS-LAX-NRT-HKG-TPE. But, you have a few segments left to use in N. America.