OpenSSL 1.0.1 should be supported, it doesn't seem an issue related to it.
@schneuwlym : you list in the message flow that Kamailio uses 192.168.1.1 at the top of the initial comment, but then you also say "Interestingly Kamailio does not listen on interface 192.168.1.1, so why does it use this socket?"
If you don't have listen for that IP, what is in kamailio.cfg? No "listen" parameter?