Which lenses for Africa is a regular topic. One not only has to consider image quality but performance with a TC(s) and not least ergonomics. The latter includes flying.
Thom Hogan also has some guidelines on aspects of travel etc mainly Botswana which is similar in many aspects.
Some of us in African savannas hike to find subjects, as much as/more than from a vehicle. So more reach is often important unless one is relying on stealth for close ups etc. I carry either a 800mm rig [400 f2.8E+TC2] with a D850, or a 500 PF with TC14 as backup to be lighter. And I try have 2 rigs (70-200 f2.8E or 300 PF on one camera with longer telephoto on the other). On longer trips I also have a 18-35 G and 58 1.4G, and a Micro-Nikkor at least, sometimes more UWIde options for landscapes. Packing depends on where and how and for how long.... When feasible, I plan to upgrade/expand the latter to a Z 14-30 f4S and 24-105 S.
As to which focal lengths, model etc it is easy to get overwhelmed with the options and also the flood of all-knowing advice. I suggest spend some time on your research. The sites to rely on (besides Steve's) include Brad Hill's, Thom Hogan's and also Photography Life reviews by Nasim Mansurov and technique articles.
300mm is fine for many larger mammal subjects in Africa. The TC's are often vital to extend a telephoto as only one heavy lens is practical to fly and carry. For birds 500mm is often the minimum; 600 is better; 800 even better..... Remember IQ with a respective TC and its lens drops off significantly with subject distance (beyond ~30 usually and 40m at most). However, I've never tested a 800 f5.6E + bespoke TC125 for IQ vs subject distance in the bush (I keep looking for a sponsor for this one!)
When the dust as settled, the 70-200 f2.8E seems to be the best zoom out there with TC14 III, not so good with TC2 III (but it can work in a squeeze). IME my copy TC17II on this lens is useless, but this may well be copy variation, which is reported with Nikon's teleconverters. Oh and the few reports, only Brad Hill actually, also say glowing reports on the new pricey 120-300 f2.8E FL SR.
So yes, another big plus for the 300 f2.8G. It is a superb optic, especially as Nikon optimized its VR II model with the latest TC2 III (read about it in Nasim's reviews on PL) so you have your 600 f5.6. It is also easier to handhold than the heavier rigs, although compared to a 400 f2.8E, the 300 is actually more end heavy (as is the extended 200-500 IMHO). My 300 gave many keepers, and I bought both TC2 and 300 f2.8G used and 2 years later got a decent tradein deal on the lens.
The 300 PF is yet another excellent option, one of the most versatile lens yet made in the history of photography. But it's pushing it at 600 f8, however. I always try to have my 300 PF in the bag. The benefits have been rhapsodized about many times including very good IQ with TC14 III and surprisingly (to me) TC17 II. It also great for closeups of plants and larger insects, herps etc, which can be refined/tightened up with an Ext ring.
It sounds like you are already very well equipped. I often use the 70-200+TC14 III as a backup/alternative, with the 400 for reach and its sui generis is the high TCF and decent IQ with all 3 TCs. But besides big expense it's more 1kg to fly with and deploy above. As we know the D500 with D850 is an unbeatable combination unless one really has to have decent silent-shooting.
So to cut the waffle, get a 300 f2.8G VRII with TC14 III and TC2 III. But if you can afford it, the other option is a 500 PF. This will also deliver very very well. Again, either telephoto will pair very well with your 70-200 f2.8. Never underestimate the 200-500 either - probably the biggest bang for the buck for wildlife, and it is popular across Africa too.
Last but definitely NOT least - etc, Test and AFFT the rigs with each TC on a standard target, then go out and Field Test and Practice, if possible shoot anything out there every day. Enjoy
The more you read, the more you think about new kit, very happy with the 300 2.8 on it own but IQ has not always been great when used with the 1.4 II TC and never with the 2.0 III TC [more than likely my technique on my Gitzo monopod as I don't own a tripod]
The 500 f/5.6 PF looks interesting but I will need to trade in the 200-500 f/5.6 to cover some of the cost and start saving
The thinking on the longer lens is driven by a booked Masai Mari safari in October held over from last year and more than likely going to be moved back again
Very happy with my D500, D850, 24-70 2.8 , 70-200 2.8
Thank you all for sharing your views
Very good you promoted the 80-400 G, and I recall 
