Render/swap templates for each user in a room simultaneously

I’m trying to swap three templates, one after the next, simultaneously for each user in a room once a timer has gone down and some simple data is collected. Disregarding the data and timer part, what’s the best way to render one template after the next simultaneously for each user? Routes would be /game/_id/play > /game/_id/vote > /game/_id/score and repeat.

I’m using Iron:router which has waitOn, action, onBeforeAction, onAfterAction, next and go so I’m having trouble figuring out which one to use. Perhaps I should use Route controllers along with the following functions?

You could trigger rendering a new template via Blaze.render() after whatever happens that should move the user from one ‘room’ to the next.