The general rule on safari is you can never have enough length. One thing is often missed is that a lot of action happens when the lighting is poor, dawn dusk etc. An f5.6 lens will struggle in these conditions.
Totally agreed, which is why I didn't end up getting the 80-400 Nikon and went for the sigma instead (and it being significantly sharper).
The sigma 120-300 was updated a year or 2 ago. The latest version has significantly improved optics but is also expensive. The older (second version) lens may be available second hand. If you go this root make sure you take a beanbag or monopod to support the lens. F2.8 will be useful, yes you lose focal length but cropping is a lot easier than noise reduction in post.
A spare body is also worth consideration. Murphy's law says that if you only take one body you will get dust on the sensor or worse.
There are actually three 120-300s, the first one to be released was the non OS version which was Ok but pretty soft in places and had no OS. The second one had OS and the optics had a significant upgrade (released about 3 years ago). The third one is the OS "sport", released last year it's essentially the same as the older OS but has weather sealing, a slight optics change and can now be configured using the USB dock you can buy. The upgrade hasn't really changed the optic quality though (the original OS is tack sharp anyway) but the weather sealing is a benefit.
The second two are both worthy lenses and great options, but the third one will be like the teeth of hens teeth to get hold of used (it's over £2500 new), the second one is only as rare as hens teeth used and will cost about £1k... Ignore the first one unless you must have 300 f/2.8 as its not brilliant.
I took both a beanbag and a monopod with me and used neither more than once. When walking I found a rapid strap and holding normally was the easiest option, it gave greater mobility than a monopod and when I was in vehicles they weren't set up for bean bags so it was useless, in other vehicles it may be better. A tripod is a great investment, I use a 190CX with mine as its light and sturdy and obviously good for lower light times and when staking somewhere out for a while. I know that advice might be contentious but that's what I find best for me after owning the lens for 2 years now.
Edit: oh, and if you do end up buying a 120-300 then check for back focusing. It's a fairly common problem on at least the second version (not sure about the third as I haven't looked). It's easy to fix though, either with microadjust in camera or send it to Sigma in Welwyn and they will do it for you for about £30 (IIRC).