Is there a firewall between your Kerio Connect server and the Internet? Many firewalls nowadays offer "SMTP" proxy functionality which is nothing else than a mail relay and some checks. So you could use that one.
It would still be interesting to solve the underlying problem. Do you have any debug logs with "SMTP Client" switched on? These could show why and where you get the timeouts.
Dexion Services AG - IT Support Services in Basel, Switzerland https://dexionag.ch