In two days, I'll be on my way for my first safari. I made the decision at the end of January at SCI. However, I had unbelievable difficulty in booking the flights. Part of the reason for the difficulty was some quirks in United's reservation system. However, I finally got reservations at the end of February. In order to put the trip together, I ended up flying through London Heathrow and I have a 15 hour layover there on the outbound segment (groan). Other airlines may have better availability, but my combination of United and SAA was crazy busy. I fly a lot and I have never encountered this kind of problem anywhere else in the world. I suspect that Alaska during the peak tourist season (June - August) would be similar.
I ended up using frequent flyer miles for the trip. Normally, that can make it harder to find flights. However, in this case, it made absolutely no difference. I only decided to use miles after we had found an itinerary that would work.
The lesson that I learned from this is that to have the best options for flights to Africa, you should make your flight arrangements as soon as you possibly can after booking the hunt. Airlines will allow reservations to be made 1 year prior to travel. If you are booking a cancellation hunt, be sure that you can actually get there.