Private worlds with very short turnover are almost always the best worlds. A few examples are American Pastime, Gehrig, Cooperstown...
Those worlds restart almost immediately. But the reason they turn around quickly is that owners don't leave. So they aren't easy to get into.
So usually the best you can do is look at the Classifieds and look for commissioners that work hard to fill open worlds. aaronbrown99 is one I see a lot with Glavine300 and Raines. KSBeachBums for Gibson are some examples.
Those worlds might not roll immediately, but they don't sit for more than a week. And if you've been in a world with a 7 week extra wait, you'll appreciate that.