Might I make a suggestion?
Scrap the 'timing' completely - instead make this a 'classic gaming club', where people would be free to suggest a game by starting a thread, and then whenever anyone felt like playing that game and/or contributing to the thread, they'd just jump right in, whenever it suited them.
More popular games would naturally trickle to the top of the forum, as they would receive more frequent posts.
It would also be useful for helping people to 'modernise' their classic games, as for example, responses to the game-thread might provide links/advice on things like widescreen support, enhanced graphics, getting games running with Vista/Win7 and so on.
To make it work, forumites would have to be tolerant of necro-posting. For example, Stalker SOC was one of the games a few months back. I'd like to feel I could play that in a couple of months (which I intend to do) and then contribute to that thread without being subject to the old flamethrower.
Just my 2 Eurocents...
A system like this would also mean no one would have to take on the burden of administration/polls etc.
People would just declare themselve as the 'champion' of a particular game by starting a thread for it, saying why they think others should play it, pointing at where to get the game, and include whatever links/advice they have discovered for bringing the game up to date.