@dgluhak4 Success! After getting control of the console serial by adding the wires to the Power Dock, I found that typing "wifisetup" would allow me to re-enter the required data for the Omega2+ to re-establish the wireless connection to my router. My system is responding normally again, and I can finally get back to the Omega configuration page:
Here is how I added the wires:
According to the documentation I found here, just plug in an antenna and you are good to go (bold text is mine):
Connect an external antenna to the Omega’s male surface-mounted U.FL connector. An external antenna can be used to extend the range of WiFi connectivity or provide a very directional signal. If a U.FL antenna is plugged in, it will be used as the default antenna, no setup required.