This is a problem across all the oneworld airlines (and indeed with Star carriers) due to the way that they share top tier information. Carriers send update files with varying frequency, and varying levels of accuracy, to a central database which is then pushed back out to the other carriers on a pre-determined schedule. That information then has to be reconciled in each other carrier's system, so there are a lot of steps involved when there's a change in status for top tier members. If the change in status occurred in March and it's still not showing...that really just highlights the problem.

This is why the AA status is not being recognized by the other partners before travel commences. But, typically, when the flights move from reservations into the departure control system, it will do a refresh and be recognized.

As you say, if you have the accurate membership card reflecting correct status, this will grant you the entitled benefits. Worst case, BA/QF/whoever can phone their help desk in order to verify your status with AA and you'll be on your way into the lounge, etc.