You can force all flavors of webmail to use secure connections by using .htaccess redirects. Note that you'll need to install a Secure Certificate for your hostname to respond on port port 443. Installing a Certificate to work with DirectAdmin on port 2222 doesn't automatically encrypt traffic on port 443. You can use the same Certificate but you'll need to install it in Apache as well.
If you don't know how to do it, you can get a Certificate installed by me starting at us$45 with installation; email me for more information.
You'll then need to tell all your clients to to get their email using your servername instead of, for example, mail.example.com, to avoid errors.
And while this will encrypt email travelling over the last hop, between your server and your client, it will NOT encrypt email travelling over the Internet, between servers. There's no email protocol for that which I know of; someone correct me if I'm wrong. That generally requires plugins to local mail programs, to encrypt mail as it gets sent, and to decrypt it as it's received.
And unless you can find something available from the publishers of one of the webmail clients you may not even be able to encrypt/decrypt email from within any webmail client; it may be available but I'm not familiar with it.
As far as SSL with IMAP, POP3, and SMTP is concerned, the setting you're thinking of and probably using do NOT encrypt the email itself, only the login handshake. There may very well be a way to protect the transfer of email, but I'm not familiar with it; hopefully someone else is.
As far as HIPAA requirements are concerned, I'd stay far away from offering it myself, the penalties for failure are very expensive. Probably you're better off pointing your clients toward a vendor of HIPAA compliant solutions and avoiding the regulatory headaches.
Security vs ease of use represents a tradeoff you might not want to get involved in unless you're going to specialize in it and climb the learning curve.
Jeff