How much overhead is there in persistent connections

Use socket.io and configure it to do polling over a 5 minute interval as the websocket fallback.

Seriously websockets are awesome, use them if possible and fallback to something that has an acceptable server load.

because worst case this thing is going to keep the http connections open for an extended duration

If this brings your web server to it's knees then your web server is a crap one. Get one that can handle open sockets and scale.

Your game object would typically be a separate prototype function (class). It might look like this:

Game = function() {
  var sockets = [];
  var pendingEvents = [];
  var interval = 500; // Process every 0.5s

  var init = function() {
    // Do game initialization stuff here

    // Start the game timer
    setInterval(function() {
      gameLoop();
    });
  };

  // Do the actual game loop
  gameLoop = function() {
     // Do some work

     // Handle user events, starting with the oldest
     var message = pendingEvents.shift();
     while ( null != message ) {
         handleMessage(message.socket, message.data);
         var message = pendingEvents.shift();
     }

     // Do other stuff
  };

  // Process a player's message event
  handleMessage = function(socket, data) {
  };

  addSocket = function(socket) {
      sockets.push(socket);
  };

  queueEvent = function(event) {
      pendingEvents.queue(event);
  };

  return {
    queueEvent: queueEvent,
    addSocket: addSocket
  };
}

This game class gives you a skeleton that holds all the connected sockets (loop through to send a message to everyone) and does some game logic every 500ms. During the game loop it looks in the message queue for player events it needs to handle.

Now going back to your original socket code, you can inject player events into the game like this:

// This happens anywhere
var gameInstance = new Game();

// Now watch for sockets
io.sockets.on('connection', function(socket) {
  // Add the socket to the game
  gameInstance.addSocket(socket);

  socket.on('event', function(data) {
    // Push the client event to the game, game will handle it on its own terms
    gameInstance.queueEvent({
      socket: socket,
      data: data
    });
  }); 
}