You should probably
start in South Africa (to reduce cost) and head to AMM

1. -xLHR or xMAD,
2. -AMM do the AMM-CAI as a side trip.
3. -DEL head to India (from AMM), do India & Nepal as a side trip.
4. -HKG head to Hong Kong and do the SE Asia part of the trip.
5. -SYD Once you are done head to south (try to go from HKG) and do Australia.
6. -SCL try to get on the direct flight to SCL.
7. -IPC head to Easter Island
8. -LIM and return to Lima
9. -EZE Fly to "deep" South America and do the rest of South America and return to the starting point.
10. -JFK (I think there is a direct flight) and do do the east cost you should also add MEX as a side trip (otherwise it will cost you about 4 sectors).
11. -LAX Head to the west cost,
12. -xLHR Return to Africa (a must) via London
13. -NBO

This will give you the ability to add three sectors when the side trips are most expensive.

Good lu