If there is evidence that there are ways to permanently improve conditions to that extent for that cheap

This is intriguing, but what if the main indirect cause of death in Africa is overpopulation?

I am not an expert on development in Africa, but my guess is that there is no single cause to the overall problem. Africa's population density is 26 people per km^2 source, whereas the EU's population density is 114 people per km^2 Source. Thus it is probably the case that Africa could easily sustain its current population if it were more economically developed.

Reducing the population artificially, whether by force or by education wouldn't make the problem magically go away, though it may help as part of an overall strategy.

If one is interested in charitable projects to improve overall African standards of living, take a look at the Copenhagen Consensus. Improvements in infrastructure, peacekeeping, health and womens' education are all needed.