You don't need to poll. One can subscribe to storage events, and that way you can broadcast ordered messages to all your tabs without any polling.
When the tabs receive the event, they each wait X milliseconds. The first timer to expire marks the event as "played". Other tabs receive this event, and abort their timers.
If a "leader" disappears, it will simply fall to a tab with a larger delay.
[1] Something like, rounded to 50ms increments, in a range, 100 - 1000ms. Avoiding collisions / ensuring uniqueness is left as an exercise for the reader.