If you are prepared to pay the AUD600 for the World Traveller Plus upgrade from ZA to UK, then you could change it to CPT-LHR-MAD rather than CPT-JNB-MAD and upgrade the CPT-LHR flight

Your qpoint /miles earning for these flights will be
50% of 5621 for the SYD-JNB = 2811 qpoints and miles for QF
for CPT-LHR will earn 150% of 6862 qpoints = 10,293
The mileage earning will be 210% of 6862 = 14,411 ( base of 6862 plus 10% WT+ bonus plus 100% bonus for completing the challenge )

Once these 2 flights have credited, you will have AA Platinum

To help your mileage earning, you might also like to consider changing ARN-HEL-JFK-LIM to be ARN-LHR-JFK-LIM using AA codeshare on ARN-LHR , AA to JFK and then LA to LIM

You may also need to purchase 1 sector within Europe since you would exceed 4, but pick a cheap sector and it wont cost much. The WT+ upgrade is a good way to go imo since (a) it is much more pleasant way to fly than in economy imo and (b) will allow you to earn 210% mileage for the flight rather than the 25% qpoints and miles which you would earn in BA economy

Dave