I checked some more online resources and found that the behavior I described can occur when the AC adaptor does supply enough current. Turns out, 500ma is about the minimum CZ-101 needs to operate properly and I had only tried adaptors that were rated less than this. I looked through my adapters and found one that could supply up to 850ma and the CZ powered right up when I connected it.
So, it was just user error. :-}
Anyway, I hope this experience helps someone else who encounters the same problem.