I'm still not entirely clear on which part of the configuration you need. If you need information on configuring BIG-IP to 'route' traffic that doesn't match one of your specific virtual servers, take a look at K7595 which describes how to configure Forwarding IP virtual servers. The forwarding server can be configured to handle traffic destined for certain subnets (or even 0.0.0.0/0).
K7595 also has a section on Emulating stateless IP routing using the loose initiation/close options.
Per the order of precedence in K14800 your more-specific virtuals will be matched first assuming your forwarding IP virtuals are less-specific. So traffic to your configured services will match those first, and other traffic will be candidate to match your forwarding virtuals.
There may be other solutions available, such as simply using a SNAT for traffic that needs to traverse the BIG-IP. Depends on your requirements.