Uh-oh. You want JNB to USA with AS miles? With AS miles your only options are BA, Cathay, Condor & Emirates. Here:
https://www.alaskaair.com/content/mileage-plan/use-miles/award-charts select region of origin to region of destination to see who they allow you to fly. Other partners won’t be allowed.
I booked Cathay with AS miles JNB -LAX via HKG (HKG is their hub). Free stopover in HKG to boot when you book via AS! Use BA site to search for availability one segment at a time. They only do biz class JNB-HKG, I did re-book it for $100 fee to a First Class ticket when I saw first class open up to LAX (no discount on it though even though only half the trip will be first). AS stopovers can be as long as you want. I’m spending a week & a half in HK.
If you find availability you may need to HUCA to book it, my first rep swore up & down it couldn’t be booked, the next one was wiser and was able to find what I saw. She did quote me the price for 2 awards due to the stopover but I explained it was allowed and she looked it up and put it all in the computer and confirmed it was indeed allowed.
(Make sure you watch what the taxes & fees are on BA flights. They’re known to be sky-high for biz/first & over the last couple weeks jumped again putting them close to “insane” territory.)
ETA: CPT could be an option over JNB, flights between the 2 cities are numerous and super cheap.