When you enable the jvmRoute feature, every response will carry a JSESSIONID cookie. This is because even though the session id remains constant (when you resume a session), the jvmRoute portion appended to it (separated by ".") may vary: It will change each time a failover has occurred.
As for the cookie's path, I think I know what the problem is: Since your webapp has been deployed at "/", the cookie's path should have been set to "/", instead of the empty string. I will fix this.
Can you deploy your webapp at a regular context root and see if you get the expected behaviour with respect to the cookie's path?
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