Steve,

Africa is a big continent and ammo availability varies from area to area and country to country. For example, if you hunted the lowveld of South Africa, you'd probably be able to get ammo for most calibres including your 340 Weatherby, esp if you went to someone like Sabi Rifles in Nelspruit. However, in Tanzania, you'd probably be able to get 416 ammo but not 340.