Here's one idea (I'm assuming DFW as the starting point):
Get a cheapo ticket dfw (AA) lhr (BA) jnb= 20,728 mls roundtrip = 10,364 Q-points
Get an F OWE ex-JNB with a routing like jnb-hkg-bom-hkg-del-hkg-jfk-sju-lax-dfw-anc-dfw-lax-lhr-dxb-lhr-hel-lhr-cpt-dur-jnb = 59,857 mls = 89,785 Q-points.
Total Q-points = 100,149 = EXP!
The fare is much lower ex-JNB than ex-USA, and you get your two parts of the trip automatically. You can do the outbound cheapo DFW-JNB + the OWE JNB-DFW in one (looong) weekend, stay in the US a while, then do the OWE DFW-JNB + the homebound cheapo JNB-DFW in another (looong) weekend.
If westbound travel is easier on your jetlag you can of course do the RTW in the opposite direction.
Have fun!