How should I debug AFP issues?
It turns out that, as I suspected, a paranoid security configuration was preventing AFP from working.

In particular, the machine had been "hardened" per Apple's security configuration guide in which chapter 9 describes how to disable AFP by unloading the com.apple.afpfs_afpLoad dæmon (I had thought it was only required to serve files, not also to connect to an AFP server as a client).  Reenabling the dæmon resolved the issue.

I am nevertheless curious what tools are recommended for tracing file sharing problems in the future.