If the certificates from the certificate chain are not listed as trusted in the Java key store, then the request will fail. This is the way the JVM works (which is where CF is running). If you are using a self-signed certificate or a certificate from a certificate authority that is not trusted by the JVM, then it will fail, every time.
There was also a bug in CF9 Enterprise which would sometimes result in a certificate not being accepted, but I believe that has been fixed in CF10. It was acutally a problem with a 3rd party crypto library that was included in CF enterprise.
So, chances are that you are goign to need to imort one or more certificates into the JVM keystore. You said you've already found sintructions on how to do that, so I won't rehash. If it is a self-signed cert, you will need to import that. If it is a cert with a CA parent, then you should just be able to install the CA root cert.
Hope this helps.
Jason