UPDATE: So no resolution found yet, however I was instructed by another player to join a large group in the desert zone and then travel to a player in the group and leave. After getting to the location of the group and clicking leave my game client froze and disconnected me, dropping me back to the login screen. When I logged back in I was no longer in the group, however the infinite auto queue was back - this solution did not work for me.

UPDATE 2: I received a response from Customer Support with the following instructions:
"Please try having another player invite you to group, and then queue as a group for the Dungeon. Once done, check your notifications and see if the option to join the Dungeon becomes available. If it does, decline, and then leave group, which should then allow you to queue as normal."

After following these instructions my character was able to queue for a Dungeon as expected, and the unending queue did not return after I restarted the game client and logged back in.

Thank you to the Elder Scrolls Online Team for your help in resolving this issue!