Default Gateway / IP Address Issue

If you have managed to connect to a different gateway, those cables do not go where you expected, or you have not connected to your main Router, or that Router has no internal connection between Wi-Fi part of the Network and the Ethernet part of the network.

There should be only one Router dispensing DHCP addresses, and all others should be set up as access points, merely passing along everything to the main Router. Otherwise you create multiple non-communicating networks.

what did you plug the other end of the Ethernet cable into?

If your own Router, then you have not made the Internal connection ("Bridged") the Ethernet Network onto your Main Network. This would be done in configuring your Router.

<<however the Gateway was a different Class C subnet than my home network >>

Then you have not connected in the way you intended, possibly due to Router configuration issues.

At the Gateway Router, your Ethernet Network could be configured as an independent, stand-alone network, or you perhaps you have overlooked the (often obscure) way the Router manufacturer intended you to connect all media into one Network, sometimes referred to as "bridging" all the various media together.

I faced exactly that as my issue when I added another Router to my network, and wanted to charge the way all the media inter-operated.

so how did you solve that?

Can you change settings in the Ooma Hub, or did you have to re-wire around that Hub?