It should be possible to enhance cpanelproxy to cope with the SSL versions of cpanel and WHM (not sure if an SSL version of WHM exists).
However, why would you bother? Modern switch technology makes it really hard to listen in on network traffic, and unless your network is highly insecure I'd worry more about securing the endpoints (PC, server) rather than the transmission medium.
I haven't tried it; you'll have to enhance cpanelproxy to add those ports. That is, you'll have to add some code to cpanelproxy.php.
The enhancement is pretty straightforward if you are familiar with PHP. You just need to add the "host" variable and a case in a switch statement; search for "2082" in the source to find where to change it. Then set up your CNAMEs in DNS and you should be fine.
Sorry: typo - "(not sure if an SSL version of WHM exists)" should have been "(not sure if an SSL version of webmail exists)"!
I rethought this a little since posting the earlier message. It may not be as easy as changing the script in the way I suggested -- the script only deals with the part of the data path that lives on the server, so channelling that through the encrypted ports is useless (and you'd need to use curl too). D'oh!!
However, if you think about it, if you have a certificate for abc.net, in theory you should be able to get https://cpanel.abc.net to work. This should encrypt the tunnel back to the server, which is what you want, and on the server it should proxy through to cpanel.
I tried and it didn't work (it went to the default page for that IP address rather than cpanel), so perhaps thats where we should focus our attention. It'll be something missing/wrong in httpd.conf ...
Gotta make sure we reflect this change back to the author's website too!