I think a good option would be to have a settings tab where you could allocate your preferred 12 hour period to have games.

For example, I am a evening/night person and worker - so any game that I have scheduled between 06:00 and 12:00 I often miss as I will be asleep. At the same time, I never get games after 22:00 hours on a day - but would happily take a game between 22:00 and 02:00 in the morning.

If you were able to give a preference of a 12 hour window in which you would prefer to play games then I think that would help. All T11 would have to do for the likes of Cat who are playing in a different time zone window is then find others that have the same preference as her - or those that are nearest to it, so everyone is able to play two games if needed a day, during hours that are convenient for them.