Just got off a call with a few of the Eshtek guys, they set me straight very quickly. Before I called them, I dove into what others here have done. Here is what fixed the router swap for me:
Sign into the TrueNas Scale Web UI.
Go to Network:
Go to Global Config settings:
Change Nameserver1 and IPv4 Default Gateway to the IP address on/of your router.
My issue was that I kept changing the NAS IP address to the IP of the NAS, not the router. Essentially, I was signed into my router interface, looked up what the NAS IP address was, and kept changing the Nameserver1 and Default gateway to that IP, when I should have been setting it to the IP of the router.
Once that is done, my NAS found the internet again, the HexOS deck found a server and I was set! I had to skip the initial setup in order to prevent wiping the drives, but I was saved. Thanks to Nick and Eric!