I might be getting a bit optimistic here but it appears one can do Africa without getting a visa in advance in Pakistan. No, not all African countries give a visa on arrival but if you plan carefully, it seems possible to land in a country in East Africa, making your way to the south, and then taking a flight back home from a West African country. The return air ticket is just above $1000, which is also not bad.

All in all, it seems like a good travel plan. Will keep you posted.