Largely copied and pasted from my reply to a similar request, this applies if you are willing to go after UA miles pretty aggressively for the next few months:

Read this post http://travelisfree.com/2013/12/27/c...routing-rules/ as many times as necessary, and collect as many a total of 320K UA/Chase UR points in one account, or 160 each in two accounts. Not too difficult with all the different Chase cards and office supply promos. Then book business class tickets that give you the bulk of your travel, say US-Asia(stopover)-Africa-US. Collect AA and BA miles, and use any leftover other miles and paid LCCs, to fill in the gaps.

US currently has similarly favorable routing rules as has been pointed out, so if there are available seats on Oneworld carriers you create a similar itinerary with a stopover that takes care of most of the longer flights.