Don't get me wrong. I totally agree that you made the right choice, especially for the node knockout.
This might be completely over the top but perhaps you should look into lag compensation technique that FPS games use. There is a global state on the server and the clients send their command with a timestamp. The server then looks at the global state XXXms ago.
You're going to need global state and scoring if you ever want a leaderboard (otherwise people will just game it).
You could also just make it so that it doesn't show the clock during the last three seconds or something. Show "calculating..." or something and give people whatever the greatest lag time is grace period.
Anyway, great game. You got my vote.