I found another lab procedure for a caffeine extraction in "Experimental Organic Chemistry", Durst & Gokel, 2nd ed.
They extracted the caffeine with an aqueous Na2CO3 solution, then extracted the caffeine with dichloromethane (DCM).
This procedure specifically warned that this system is likely to form very troublesome emulsions, so you should mix gently. On the other hand, I was following the advice from another book re sep funnel usage, "Really shake it!!".
One question: The book had this as a problem, with no answer:
Why would you extract with a basic solution? I would expect that, in acid, the N on caffeine gets protonated and the result is more soluble in water, than when the N is not proronated. Using the basic solution did seem to work, but I don't understand why acid wouldn't have been preferred for the extraction.