Well, everybody has their priorities, but in terms of impromptu-ish design contests three months is really unheard of insofar as contest durations are concerned. I mean, look at the various Game Chef competitions and the 24-Hour RPG competition. Or even the various Story Games competitions.
Don't get me wrong, I hear where you're coming from (I, too, have a 40+ hour-a-week day job, numerous civic duties to attend to in my free time, and personal projects to work on), but a big part of the challenge for such contests is the limited time windows. And the challenge is what draws most of the participants.
Giving somebody three months to design a game isn't really all that challenging and, I suspect, might cut down on the number of interested parties (frex, I'd have no interest in submitting to a contest with that time-frame, even with my harried schedule, though I might volunteer to serve as a judge).
I freely admit that I could be wrong, but I don't think it's coincidence that most of the successful and well-known game design contests have a narrow work window available for participants to submit within.