Just playing around with possible itineraries:

Notes:

• I assume the status you want to maximise is your QF WP status
• So you need 1200 SCs in a membership year to maintain that status
• A well constructed 1st class itinerary should net you much more than that
• Depending on when your membership anniversay date falls in relation to your trip break back in Texas
• I assume you'll be looking to earn 1200 SCs either side of that date - so that you maintain status for 2 years

Here's a non-optimised 14-segment AONE6 ex-Jordan intinerary that will more or less do the trick for you AMM-MCT-LHR-SYD-HKG-JFK-DFW-JFK-GRU-xJFK-xLHR-DAR-JNB-LHR-AUH

The final few segments (GRU-xJFK-xLHR-AUH) show transits at JFK and LHR - these are required because they are second visits to those continents (see rule 4e).

I show AUH as the final stop - just to highlight that you don't need to return to AMM - anywhere in the Middle East is allowed (rule 4c).