Were you able to resolve this issue? I'm asking because I'm currently experiencing the same problem. I've spent several hours trying to figure this out with no success. This first appeared after I upgraded the JSS and clients to version 9.96. Any help would be great. Thanks!
@bentoms - I'm still struggling to recall but I'm fairly sure the issue was that we had those ciphers plus some old ones mixed in, I had to remove the old ones before the binary and Self-Service started working correctly.
Our issue was that we did the JSS upgrade - all of a sudden Self-Service policies weren't working. The logs on the local machine kept showing a handshake error (slightly different than OPs) every time a policy was called via SS.
I think the tl;dr of it was that we needed to upgrade our Java version because older versions of Java needed to use an old cipher which was upsetting Self-Service. Once we updated Java (and removed the old ciphers) I think everything was fine. Man it feels like forever ago.