I've found that some of these will work with, e.g. Dovecot's IMAPS daemon, just by appending ":993" to the hostname.
Yesterday I found one that would only work on port 443, but it was a simple matter of creating two iptables rules: one to permit incoming IP packets to 443/TCP and the other to redirect them to 993/TCP.
Not to my knowledge; a full testing tool for IMAP, SMTP, TLS, DKIM, and DNSSEC would have been amazing a year or so ago when I was still maintaining mail servers!