I have weird but good news. Today, after reading tyche's reply, and after my many failed attempts mentioned earlier in this thread, I opened Stanza on my iPhone to create a book source for Calibre.
The "books in calibre" item showed as before, and I clicked on it... and it instantly showed my Calibre catalog. The speed is particularly impressive, since I have over 2500 items in Calibre currently.
I have no idea why it suddenly started working today, but I'm pleased it is. Puzzled, but pleased.
