Wow -- thanks for the advice. The IATA database was particularly helpful -- thanks.
Two of the countries (Kenya and Tanzania) state that they require 6 months left on the passport. I presume the 6 month rule is usually set in stone?

Unfortunately, I'm right up under the 2 week deadline. The closest passport center (Chicago) doesn't have an in-person appointment until March 23. Do they process in-person requests on the same day?

Argh. I really could have planned this better, so I appreciate the advice