I just found that instead of restricting the available ciphers on the Tomcat server as per comment #6 I am also able to workaround the problem by just restricting the available ciphers that the Apache proxy uses by adding "SSLProxyCipherSuite RC4-SHA" to my Apache VirtualHost config. This makes more sense to me to since the problem is with the new server rather than with the old Tomcat server. (At least that's my understanding.)
I just found that instead of restricting the available ciphers on the Tomcat server as per comment #6 I am also able to workaround the problem by just restricting the available ciphers that the Apache proxy uses by adding "SSLProxyCipher Suite RC4-SHA" to my Apache VirtualHost config. This makes more sense to me to since the problem is with the new server rather than with the old Tomcat server. (At least that's my understanding.)