I have been watching and eagle's nest for a short time and was treated to an aerial display by some eaglets learning to protect themselves while flying. These were shot with a Canon 5D MIV and a 600mm f/4. The 600mm was on loan through the Canon CPS program. All images were cropped due to the distance of the eagles.
I have been with (https://www.facebook.com/peterswildlifesafaris/ ) and found Peter to be great. I have been to Africa with a different tour and found Peter's to be the best. If you have any questions please let me know.
I just got back from doing the Upper Antelope tour in Nov.. You camera and lens will be fine. The only suggestion I would have is that if you plan on doing brackets limit it to three shots one stop on each side of 0. I tried two stops and it took to long. Plan on shooting with an ISO of 800 and f/11 or something in that range. Know your camera when you get in there they will limit your time to 2 minutes on some shots where they stop the groups of other people so no one will be in your shot. I went on the first tour of the mourning and there were only two of use on the photography tour.
I have been to Kenya twice and have the same cameras you are looking to take. If you are looking to to take three lens then I would do the 24-105, 70-200 and the 100-400. With the extenders you should cover everything you would need most of the time.
I have posted a download it 6000x1500 pixals. I did not think I could post the file 26844x6742. The reason I have 32 images is that I shot the photos while turning the camera and shooting at slow continuous shutter speed of 1/1250 to try and capture the waves coming in. The lens was a Canon 24-70 f/4 at 50mm f/13.