Curious where you are planning to hunt buffalo in central Namibia? The only non "put and take" option that I know of outside the Caprivi is the Waterberg Plateau National Park. A very unique (and expensive) destination, but an opportunity to take a monstrous bull. That outfitter would have the other classic Namibian game in the same area. The Caprivi is the more typical Namibian destination for buffalo. I can speak from personal experience that it is a fabulous hunting environment for buffalo (essentially the Okavongo ecosystem), and all those outfitter’s who operate there would be prepared to combine a buffalo with plains game further south. Jamy Traut is a good person with whom to begin a dialogue.
https://jamyhunts.com/ I know he hunts the Caprivi, and I believe that he has just acquired rights to the Waterberg. I can also recommend him unreservedly.
Nothing wrong with your battery. As others have noted, a .300 class rifle for PG is theoretically a better (and more traditional) choice, but your 7mm will easily get the job done, plus give you a bit of reach for those long shots in the desert or mountains. (Not sure why, but a lot of folks will criticize the 7mm mag, and then wax poetically about the 7x57)
To be fair, it is not a caliber which I personally would like to use on an eland (a classic Namibian hunt) - and a quality 175 gr load would buy you a bit more penetration.
The .404 will do the job on buffalo with ease and style.
In Namibia, waterhole shooting for doves and sand grouse can be a fun afternoon. Your twenty would do perfectly for that sort of shoot. I shot a pile with my 12 bore Paradox shooting 1 ounce loads which is essentially a 20 load. However, due to ammunition weight restrictions, it is hard to carry enough shotgun ammunition internationally for much shooting. Particularly with two rifles along. 12 bore is much easier to locate locally.
My only criticism is the amount of hardware. I hate bag dragging, and over the years and trips, anything more than one rifle has become one too-many. (Though I cheat a little and use a Blaser R8 or S2 - an extra set of barrels have found their way into my gun case). A .375 would allow you to more easily drop one rifle, and it may be that your outfitter has a usable shotgun. That said, and trying to be kind, shotguns belonging to PHs tend to be an indifferent lot.
In any case, welcome to our group and have fun planning that expedition. I have hunted Namibia four times including buffalo and leopard, so feel free to PM me with specific questions or recommendations.