Alternating would give us four weeks each. I think I'm able to play on the Friday of the Thanksgiving weekend, but I will have to talk it over with my Significant Other. I'm not sure what our plans are yet for that weekend. People who leave town to visit family might not be able to, depending on if they're driving Saturday morning...
Any input, Melbosa, Tom, Ustauk?
From some discussion in the office here, I think the second sample schedule is preferred (as it has more sessions), but Dec 28 is a no-go simply because it falls between Christmas and New Year's. That'd still leave 17 sessions.
There's also the thought of pick-up sessions; that is, sessions that are not on the official schedule but that we check to see if everyone's available and if they are and the DM/GM is ready to go, play anyway. For instance, I have so many D20 Modern thoughts running through my head right now that I could easily pop off another session this Friday or Saturday

We even talked about weeknight sessions. If we start playing at 6 and stop playing at 10, everyone'd be home by 11(ish). But some or all of you might already have stuff to do on weeknights, so I'm not sure if that'd work for anyone.