This has been happening wired, However I AM useing a powerline ethernet system, not sure if that's what's causing issues but I don't think so.
So you're saying have the modem the way it is now, and run another one on say 192.168.1.xxx hardwire that to the modem and use that instead?
Also not sure if it means anything but the modem doesnt show anything for Clients when I was using DHCP