RV - I didn't catch what country you would be hunting in? I've only been on one for much the same animals you will be hunting. I went to the Customs office at the airport with the guns l planned to take, and some I thought I might take on another trip. The Custom's agent was helpful and I found the paperwork easy to fill out, and hauling guns in an out of the office the most onerous. Having the proper forms filled out "in hand" at the airport was a real "plus".
I used South African airlines and they were used to working with hunters. Another plus, was their travel schedules kept us out of countries that are not gun friendly (England, for one). I took a .300WSM and a .30/06, but hardly used the "Mag". Most PH's seem to have a preference and will suggest "minimum" calibers, but those you have chosen will do fine. As Grumulkin has said, it is your hunt and you are to set the distance you want to shoot and what you are willing to pull the trigger on. You'll have to pay for every animal you shoot, whether you "collect it" or wound and lose it, so don't let anyone talk you into too long a shot!
I noticed you have "Warthog" on your list of animals. I did as well, and because of the FDA's policy regarding "Swine Flue" at the time, I wished I'd have taken 50 picture of my "kill" and left the warthog in S.W. Africa. It was quarantined for 5 days when I got back to the "States", even though the airlines would only store my trophies for 2 days without my incurring a "storage" fee. (They also would not release all my trophies, except through a local taxidermist because the warthog had to be "treated"; I had not made any prior arrangements!) This restriction may no longer exist, but you might check with your "carrier" or "Booking Agent". (You can have your trophies handled entirely in Africa by a taxidermist that come recommended by your PH or "agent". Worth a "look" if you don't have a local taxidermist you already trust.)
Also, if you are using "reloaded" ammunition (I did), make sure all the brass and boxes are marked and correspond with the caliber on your rifle. I know this sounds "trivial"; however, having .270Win ammo in a .30/06 box or brass stamped .25/06 (resized) confuses custom agent in some countries. When I went, I was told to pack my ammo separate from the rifles. I also used many small locks to discourage "pilfering".
I still to this day have a tendency to "over pack"; resist if you can. I did take a small range finder and found it helpful. I also wore a couple of pairs of clothes, vests, jackets, and heaviest pair of boots on my feet to avoid having to pay for extra weight. I don't know how that will be considered with the latest TSA rules, but I have not heard of a complete "strip search"
to date!
You are in for the "time of your life", in which the amount of money you have invested will go away before you step on that plane! Congratulations on your good fortune to go on this trip and may it be a most memorable event!