Have you checked AF all the way? IME ST awards are quite odd, so sometimes there is better availability for AF than for DL or anybody else. In theory AF/KL are identical but in practice sometimes availability is there for codeshares either way so I'd persist in checking every option you can dream up. I have not done CPT/JNB awards beginning in NYC but I have done from GIG. It has been surprising what can be done if you're willing to continue experimenting. Remember that AF/KL US normal reservations are handled by DL, but AF/KL directly handles their award bookings. Using DL miles in principle should not work when calling AF?KL award desk US, but I did get that done once (bizarrely, for AF A380 FC, which is said to be impossible since DL has no FC so AF will not allow it to be booked, but they did at least once).

Sadly DL no longer allows Expert Flyer or other third party award inventory checking, so you'll end out calling a few times to find out how best to make your itinerary work. Someone here may have a less-calling-intensive solution than mine.

As hints, I check normal inventory on all plausible ST flights to choose my requests based on what seems to be the least heavily booked options. One consistently available option for me has been MIA-CDG-JNB. AF has a 77W on the route that is rarely heavily booked during northern hemisphere summer months. That, of course, leaves you with finding NYC-MIA and still gives you transfer time, but is more dependable than Europe summer transfers IME.