I'm looking at just the case for voting on a post not authored by any of the players. This is unrealistic in other ways, for example, it ignores opportunity cost of voting on something else instead.
Optimal time in the 2 player game may not be an integer number of minutes, but working with countably or uncountably many strategies was something I hoped to avoid.
in that case there will be an equilibrium as long as you can squeeze all the votes before the 15 minutes I guess