I took the UA trip (including pre & post) in Oct 2011. Hopefully, these comments will be helpful.
I had previously taken the route bowenbernie suggested . . . requesting extra pages when obtaining (or renewing) your passport. That will save a lot of concern & uncertainty, but that's really advice for "the future".
I just checked my passport and found the following. Of course, you are at the mercy of the agent when entering/leaving any country. I've always been most comfortable letting the agents "do their thing" rather than requesting that they stamp specific pages etc, as has been suggested.
South Africa (altho' I entered/exited mulltiple times) only stamped 1 time (when I departed Cape Town) to return home.
Zimbabwe only used 1 page - Page B (extra pages)
Botswana only used 1 page - Page C (extra pages)
Zambia used 2 facing pages. The Visa (that I got at embassy in Wash, DC) was stamped on Page G. Page F was stamped twice, when I entered/exited. (Note that during our long layover in London, I went into the city for a couple of hours & Page F had already been stamped at Heathrow.)
OAT's printed & online handbooks for my next rrip (Affordable Peru) do not agree on everything. My experience regarding e-mail & phone calls to/from OAT has been inconsistent . . . usually, prompt, excellent & accurate, but . . . sometimes, no response . . . sometimes incomplete/incorrect info.