I've managed to get it working again, but not sure if by coincidence, or if what I did actually fixed the problem.
All I did was deselect all preferred coturns for ICE in the list, and deselect force relay connection.
You can do this by ctrl-clicking any selected coturns. Alternatively, select all of them with shift-click.
I tested that it stopped working with a single prefered coturn, and worked again by doing the above.
This seems backwards because these are the initial troubleshooting steps to take when not connecting in the first place, but this is what worked, so there you go.
Hopefully it works for you too.