If you want to be really tricky, you could just set the external network address of the core to a static IP...
Even trickier - set up advanced routing rules on your external network to access the internal network using the core as a gateway to the 192.168.80.x address space.
But then again, you could just do it the correct and simple way, and use the internal network for all devices that are talking to the core - since that's how it's supposed to work, and that's how the configuration is set up for you automatically.