You should add "democratic mode" - every button push counts as a vote for that control. An election is held every X frames.
Websockets are way easier to comprehend and implement than WebRTC (learning the connection negotiation process for NAT traversal isn't much fun). But in the end using WebRTC meant I could host a more cost effective demo that could still scale reasonably well.
Would be pretty fun once there’s more than a couple people connected.