There's surprisingly little discussion of xGLOB34 here.

I'm thinking of using a DGLOB34 to be able to visit either Tahiti or Fiji, starting in JNB.

Am I interpreting the rules correctly that I can bounce around with a TC region, e.g., between Tahiti and Asia? So, for example, I could fly LAX-NRT-PPT-HKG-JNB?

I know that I'll earn full AA miles and EQP/EQM for any AA codeshare, but what about an Air Tahiti Nui or Air Pacific flight coded as someone else such as QF? Will I earn AA EQP?

It's very hard to figure out a routing that works that lets me go to either NAN or PPT, especially if I want to stop in Los Angeles, and I'd prefer to fly AA over the water, and also prefer CX over QF for the start or end.