Client Connection Issue with SSL Cert

If you have SNAT applied, then you're looking for packets coming from the BIG-IP self-IP to the application. Packet in/out stats are great, but they're not giving you enough information here to properly troubleshoot this issue. You need to see traffic on the wire to know where it's coming from and where it's going. The fact that you see application_data traffic in the ssldump means that the SSL handshake was good and completed, and that actual (encrypted) application data was flowing from the client. I also see server-to-client application data, so it would seem suspect if there was no data seen on the server side of the proxy.

Did you by chance enable debug logging for SSL on the BIG-IP? If so, do you see anything unusual in the LTM logs?