There's a much easier way to do this, and it worked on my Moto 360 from 5.0.2 to 5.1.1:
1) Open Android Wear app
2) Click Settings in top-right (looks like a gear)
3) Choose Moto 360 under 'Device Settings'
4) Click 'Forget Watch' at the bottom
5) Go into settings of the watch and choose 'Reset device' and say yes to 'Are you sure?'
The watch will reboot and the Android Wear app will prompt you to pair with a new watch, but will eventually timeout while waiting. Once the watch is ready, click the retry in Android Wear and complete setup like before.
Once it is done, go into settings, about, system updates on the watch and it will start downloading.