Did you steal that term "pseudo live" from me?
First, I agree with fafa-fr that I don't think it's necessarily necessary to make an official new time element, because you can always get together with people, set it to turn-based, but play the game live but slowly, with breaks if you need them, etc. I do play like this cause I log in and just stay around, check back for new turns up, etc. I play live with one person, set to turn-based unlimited, so we can chat, take a break, etc., and not have to worry if we get interrupted and need to change it over to turn-based. So it certainly works without an official setting.
But if such a speed were available, my preference would be for a fast turn-based. You could maybe make something like 6 hour start time and one hour per turn, or some such. This preference is mostly because I doubt a slow live game would be good enough to allow for long breaks and the like, and "turn-based" can also be just a really slow game, rather than a game where there's only a turn a day (or less).
That said, I don't think the continent idea will necessarily work, nor the suggestion I always see about time zones. There's an underlying assumption in those suggestions that everyone works the same type of hours, works Monday thru Friday, free on weekends, and some people also assume everyone can play at work, or can't play at work. But everyone has different schedules, work different types of days, they may or may not have free time at work. Rather than making games by time zones, you could simply request a time interval for the game.
I see some problems still though. What happens if it still runs too long and someone can't stay around? It may need an option to turn it into a different turn-based speed. Varying schedules is also a problem, but I think giving a time range for the game would be helpful. I'm sure someone will think of other issues.
(Now, along the same lines, I'd love to see a slow live speed, but not really for this same reason, and I would not choose this as a solution here. But rather because I detest having a clock running and it makes me feel like I'm on hyper-drugs or something - feel like I need caffeine just to keep up. I also like to be able to chat
and think about the game. But a slow-speed live would be nice, say, double the normal speed.)