Specifically, I'm wondering if famine is not part of the natural self-regulation of the local environment to shed excess population.My answer is no, I don't think that famine is part of a natural self-regulation of the local environment, because the natural environment didn't create the violence that has been an important part of the limited food supply in these regions, nor did the environment on its own divert water resources and generate climate change. But we as humans have to be more aware that our actions have consequences and many of those consequences are bad. Too many children in an area does create a situation in which even a relatively small deviation from normal life can have harmful consequences because people are living on the edge all the time.
As you point out, all to these regions have very high fertility. If they had lower fertility is it not likely that there would be no famine, or that the famine would be much easier to address?
I recommend that everyone read "The Science of Consequences" by Susan Schneider. She reminds us of the various ways in which humans sometimes fail and sometimes succeed at figuring out the good and bad consequences of what they doing to themselves and the environment around them.
And I recommend that everyone pore over the research conducted at the Vienna Institute for Demography on the key role that education plays in almost everything demographic in the world. Increasing levels of education don't guarantee a successful future, but they dramatically increase the odds of people being healthier, having fewer children, having a more productive life, and generally improving the overall level of well-being for themselves and others. That is, in fact, another resource that should be added to the assistance package along with food and contraception.