One problem with crediting CX/JL flights to AA is that you don't get any credit for flights on either below a fairly mild discount in economy class, so the answer to that Q depends in part on what fares you expect to pay. Some of the time you can fix this by buying a flight as an AA code-share, but I suspect that's not possible for most flights within Asia that don't connect to an AA trans-Pac leg.

Besides, you'd miss out on upgrade opportunities. I'm not familiar with the CX/JL programs, but as a general rule most airlines are better about upgrades on their own flights than on partners. (That's true of AA, as you surely know. Your EXP card doesn't do you much for you in that regard with either CX or JL.)

So, if it were me, I'd compare the options and pick one. It will probably be easier to get a comp to a *A airline than within oneWorld. (I got a *A comp based on OW status within the past two weeks, though BD isn't likely to help you much.) Comping based on alliance partner status is generally not done - it's sort of like trying to date your roommate's boy/girlfriend. It's not impossible under unusual circumstances such as you describe, but won't be as straightforward.