irule to filter out all local0

How have you configured the second part - sending all syslog messages to server 3?

Again, an HSL is only going to send what you want it to send. Local0. is really irrelevant here because that's a local facility that just gets dumped to /var/log/ltm. If you want to send something specifically to a remote syslog server, your HSL command will have to define that information. You can alternately, and probably more easily, use a Request Logging profile instead of an HSL iRule. You'll need to modify the required CEF format yourself, but then the profile can be added to any VIP. See the following for more information on the Request Logging profile.

Manual Chapter: Configuring Request Logging

Also, here's an example of a CEF-like message defined in a Request Logging template:

CEF:0|F5|LTM|11.3|$BIGIP_HOSTNAME|REQUEST|Request to: $VIRTUAL_IP|info|Request from: $CLIENT_IP|Request URI: $HTTP_REQUEST