Assuming you are happy with your current body (which I know you are) then my take is always based on this question, "Are you the type of photographer who would benefit from, and would frequently carry, two cameras together?" If the answer is no, then go with the glass. If the answer is yes, then the next question is, "Am I looking to compliment my current camera or move in the direction of an upgrade?"
I love the idea of the D600 and D800 together. I'm waiting for my D600 to get back from service as I get used to my D800, but I like the idea of the less dense sensor on the D600 and it's (potential) ability to provide higher IQ due to the lower pixel density. You and I seem to have very similar interests, and for me the idea of a long lens on the D800 and a normal/wide on the D600 seem just right if I'm going to be out and about shooting.
We've been thru the "D800 as DX" elsewhere, and it makes sense that since it can do that then you don't need to look at the D7100 or D300 unless cost is a prime motivator. Given the difference in form factors and function the D600 could lead to minor frustrations while shooting (they are very different), in which case you may want to decide whether you really want a second D800 or make the move to a D4? You'd need to go used to make your budget, but if it's the one that makes sense then it makes sense.
Ultimately, it comes down to whether you want to walk around with a pair of cameras. Only you can answer that. I suspect Africa will give you your answer - unless you're trying to figure it out before you go. Maybe rent a D600 for the trip and see what's what?