Re: Email != Webmail
There's no reason why IMAP can't accept OTP. It's not something I've looked into, but I imagine it's possible to, for example, get Dovecot to use PAM for authentication and then configure the Google Authenticator PAM module.
Dovecot does seem to have a built-in OTP mechanism, but a very brief search in their documentation doesn't give any details on how it works.
If you used the PAM approach above you'd be able to configure to accept the OTP code by appending it to your password. That way you avoid having to modify the IMAP protocol in any way.