That's one of those messages, though, that has to be phrased quite carefully or it will do more damage than good. It should include a lot of empathy regarding the time zone challenges and not just be a "that's why they call it work" statement -- which doesn't answer the question you asked, so let's get to that.
What not to do: two meetings. For so many reasons, it just won't work. What it will do is divide your team into two rival teams -- exactly the wrong outcome.
Based on your description of a dozen sites involved from around the globe, I'd think the best solution would be one meeting that takes place on a rotating schedule. Rotate among three times that are each 8 hours later than the previous one, rather than two that are 12 hours apart. If you do that, then any given meeting should be during work hours for two-thirds of the participants, more or less.
As you operate by consensus, offer up the idea in your next meeting and ask everyone in attendance if someone has a better alternative. When the discussion is over, whatever alternative you end up selecting, I'd advise you to make the point that with the new schedule, your understanding is that everyone on the team is committing to attending all meetings, not just the ones that are convenient.
It might be a good idea to confirm this on a roll-call basis, by name, so that everyone publicly commits.
The only alternative I know of is, to my mind, even worse, and that's to officially move some team members to either second or third shift, depending on their location. In addition to being a bad way to treat people, for a group like this, interacting with local colleagues is more important than participating in your team meetings -- which means this solution would do more harm than good.
You'd think that for all the talk about the world being flat, globalization, location independence, and so on that someone would have figured out the technology for having the sun shine everywhere on earth at the same time, wouldn't you? It's time for the astronomers to step up to the plate and get the job done.
Until that happens, the three-time rotation I described will probably have to do.