So I just recently completed this trip minus the lax-Ny leg) on award travel.
it took some work to construct and I'm not fully sure post "exursionist perk" rules it can actually be done.
that said we had to be flexible. I searched a two month window for a ZRH/FRA to JNB flight that has two business saver seats. Once I found it I constructed the rest of the award. I didn't get me return flight home locked until about 2 days before we left on the trip when Swiss opened up more saver space.
we ended up doing the entire trip on Swiss except for the short hops from JnB-CPT.
if paying South Africans airways flies a direct flight from JFK. The seats are large and spacious, AVOD is minimal, and seats are only ok comfort wise (in business).
if you're paying cloying Lufthansa through FRA will get you on a 747i for most of the flight.
odds of upgrades with just RPU? Unlikely. On domestic maybe if you connect somewhere on the LaX-NY route but the direct is a PS flight and harder to upgrade.
if you go during their winter I'm told Lufthansa has more award seat possibilities. We went during peak summer which is why we had to wait until last second to get it booked Comm g home and then just got lucky.