Thanks everyone, from all the replies it looks like I should be able to pull it off, and probably with just the one CAT6 cable to one port on the modem. If that fails, maybe better luck using 2 CAT6 cables between modem and computer (can do another NIC, or go through a VLAN in my switch).
The real fun comes when I try to update my manual firewall rules for yet another interface, and then routing only some packets to the new interface... That is going to take some serious time.
I think I have the Hitron modem, but I'm not positive (and it's currently buried pretty well).
I'll report back if/when I make it work! Thanks!