Mgmt Auth Traffic on external VLAN

Anything that is not locally significant to the mgmt interface will need a route. An option if this is a concern is to place a linux box locally in the F5 management interface subnet and set up openvpn or similar to bind local interfaces to remote destinations. That way you won't need any routes on your LTM. I've used this in the past in DMZ environments, though supporting far more than just a few devices given the additional complexity.