Ok, after reviewing the forums, it looks like several people have had problems with imap_open under PHP. At least I feel like I have company.
Has anyone gotten it to work?I've tried LOTS of permutations of the server string, with no luck. All act as though they have crashed apache (the script does not continue after the imap_open call). All the server strings have something in common with this one (which should work): '{mail.my.host:143/notls/norsh/novalidate-cert}INBOX'
I have tried connecting to my own imap server here at home. It appears that the connection opens, but then immediately closes again.

I'm still trying to find the debugging options for the imap server, but if I get anywhere with this route I'll let people know.