The only thing I can think of would be to turn on SSL debugging on the server (javax.net.debug=all). I've done that before when I had issues establishing a TLS session with a Tibco EMS server and that was the only way for me to find out a similar mismatch of supported cipher suites.
Some more info here: http://www.herongyang.com/JDK/SSL-Socket-Communication-Debug-javax-net-debug.html