Torquewrench, regarding MAF, I think you have to more than just show your strong Christian beliefs. Also I believe you have to find sponsorship from your local church etc regarding pay. Not having a go, just saying it's not just willingness that gets you in their front left seat.
Regarding the other flying eg MSF, Oxfam, MERLIN etc etc don't have their own pilots and tend to charter aircraft. So if you have an ICAO licence and type rated on a C208, Twin Otter and similar, then try Air Serv's website.
I believe in Africa they also Nature Link pilots (on Air Serv aircraft!!) but having not been up to speed in that department it could be all changed by now.
I did 6 months as a contract pilot in the DRC and can say it was some of the best flying I've done so if you're looking for a sabbatical then enjoy. I was fortunate to be with a super group.