Hi Warthog Fixer, and welcome to NE.

There are several options, some more expensive at first glance than others.

Some of the high end makers of new Magnum length Mauser actions and/or rifles:

http://www.ritterbusch-rifles.com/?lang=en
http://www.granitemountainarms.com/
http://www.johannsen-jagd.de/grosswildbuechsen.html
http://www.satterleearms.com/index.htm
http://www.rbbigbores.com/
http://golmatic.de/Waffen_DE/jagdwaffen_de/jagdwaffen_de.htm

Other options in a 416 Rigby (although not exactly Mausers, and not take-downs) would be CZ or Ruger. These would not cost as much as the ones linked above, but might need a good gunsmith to go over them to make them 100% functional.

As for the calibers you mention, only the 416 would legally be usable on all African game. The super flat trajectory of the 338 Lapua isn't really needed in most of Africa, and is not large enough to be legal for "Dangerous Game" such as buffalo or elephant. Not to mention that if you needed to replace lost ammo (say one of your bags gets sent to Iceland instead of Zimbabwe), there is no way in hell you'd find 338 Lapua anywhere in Africa (maybe in RSA if you're lucky?), while you could get a hold of some 416 Rigby in most typical hunting countries.

Erik