Interesting. It looks like the client is attempting SSL client cert auth in one of your deployments. The process running that code must have access to a certificate with private key that has client authentication EKU and is trusted by the Sun Server.
I'm not sure why it is so slow although I've definitely seen these types of delays caused by client cert auth. Might be delay from CRL validation or something like that as CRLs are accessed via HTTP calls typically. A network sniff might show the details.
If you don't want client cert auth (and I'm guessing you don't care about it), then you might be able to disable this behavior by implementing the other callback (QueryClientCertificate or somethign like that? I don't have the docs in front of me) and basically telling the SSL stack to ignore client certs.
The Sun directory admins may also be able to disable client cert auth on their end but they might not want to because someone else might need. Best to control in client code as well.
Figuring out which cert is being used and removing it would also work although that might break something else. The option then is the attempt to permission the private key file so that the processes running your SDS.P code don't have read access to the private key file but the processes that DO need it retain access. That sounds more challenging to figure out though so hopefully the code-based solution works.