A number of GA pilots have done this; some have written articles about it, and one or two may even have written something detailed enough to be useful to somebody else.
Three problems come to mind:
avgas
avgas
avgas
I suggest you contact a specialised overflight agent e.g.
this one. The last chap I read about used one of these agents for the lot, apparently. They can fix up crew visas too; another job which is an absolute b*stard if you try it via the various 3rd world embassies of countries along the route.
I think most have done it via the east coast of Africa, thus avoiding the worst of the cannibals. Crete (Iraklion or Sitia) is easy enough and then you can zoom down to Luxor HELX which claims to have avgas. That's as far as I've looked into this kind of thing. Then you have Sudan...
Libya seems hard. To go there (Visas etc) you need to be "sponsored" by somebody there. Like EVERYTHING in Africa it can be arranged with a bundle of $$$ but when I looked into it in 2007 (for a short trip from Crete which was abandoned) it didn't seem trivial.