I called the airlines today (started with Lufthansa, whose flight these are, but had to talk to United, where I booked the ticket) to try to change to an earlier flight from Geneva to Frankfurt (there are several that day), but it would cost me $1800 in change fees and fare differences.
If we miss this connection, it gets quite difficult on the other end. The next flight to Johannesburg wouldn't be until the next day, and we'd have to try to figure out how to rebook our SAA flight from JNB to our safari destination, and we'd miss one of our only 5 days on safari. Each day is quite costly, so it would be a total bummer to miss one of those.
I'm taking my elderly parents on their "bucket list" trip while they are still healthy enough to travel, so I really want to try to make this go smoothly. Kicking myself for not booking an earlier flight from Geneva to Frankfurt, but hindsight is 20/20.