I am running into this issue because my workplace has its own IRC server which does not support SSL.

If all of the IRC servers you are using support SSL connections on port 6697, this is not really an issue because your connection will still succeed, even though it is not using the port you asked for when adding the server listing.

Does anyone know of a public IRC server which does NOT support SSL?

Using the /server command works, I can usually specify the port with /server irc.alice.net 6667

"for some reason mIRC tries to connect to irc.alice.net +6697 which could be anything"
Raccoon brings up a good point. I could theoretically set up two different IRC servers on the same host, one running on port 6667 and another running on 6697. Connecting to the different port could connect you to a different server entirely.