As suggested by some of the threads here, I contacted AA today to get them to cross-refer to my CX and UL bookings to make it easier to through check baggage.
Spoke to two agents.
The first insisted that it was not possible to through check baggage on separate bookings. Only if it was on the same ticket. My reference to the AA Agency Reference website was ignored.
HUACA much later.
The second similarly insisted that it was not possible. When I referred to the AA website, I was asked if I was calling from a travel agency.

When I continued to try to persuade the agent, I was told to contact OneWorld and that I would be provided with their contact number. I said I would be glad to have their contact number. After a long hold, I was told that there was in fact no contact number for OneWorld.
I then explained that on the OneWorld website, visitors are directed to contact the member airlines of OneWorld such as AA, CX and UL. The agent did not appear to recognise CX and UL as OneWorld airlines.
I then requested to speak to a supervisor. Initially, I was told that a supervisor would give me the same response.

When I requested to persuade the supervisor personally, I was put on hold. Another long hold later, I was informed that my CX and UL bookings would be cross-referenced in my AA booking but that there was no guarantee that my baggage would be through checked.
I guess the AA website counts as a source of misinformation as far as the call centre is concerned.
How do I check if my CX and UL bookings are indeed cross-referred in my AA booking?
Thanks for reading.