Rear projection doesn't work very well on the back side of a concave surface. The curvature can't be very high, or else the edges of the dome would lose significant amounts of brightness as well as being nearly impossible to maintain full pixel resolution. The most likely place for a projector is mounted just outside the edge of the dome, facing inwards towards the center. The technology already readily exists, is in use in many places (the Simpsons ride is similar), and works extremely effectively (see the image I posted a couple pages back).
As for the screens pivoting rather than it being a carousel, there are several problems with this. First, you'd have a transition from screen to screen, which would limits the immersion factor. It would be like passing by screens like this: OOOOOO where the sense of being immersed
inside a scene disappears every time you have to move to the next dome.
I would say it's almost a definite foregone conclusion that the screens are fixed to a carousel that will spin as the vehicles circle that carousel. It's the simplest, most effective form of immersion. It makes no sense to add in the extra complexity of articulating screens when that very act also imparts the loss of integrity in the immersion of the projection dome. Why bounce in and out of domes when you can stay immersed in one single dome?
Edit: Here's what I'm talking about: The black projector (a rear proj.) can't fully cover the entire screen. Even if you have two rear projectors - one on each side, they have the same issue - they'll "miss" the top and bottom of the dome (line of sight).
The more likely scenario is front projectors, perhaps even two like I've illustrated in green (one on each side in order to allow the vehicle - the red box - to get deeper into the dome). This would allow the vehicle to further move inside the dome to be immersed in the video. The projectors would be virtually invisible in the dark, and by the time they're turned on you're staring into the middle of the screen. You might see them if you look to your left or right, but they wouldn't be noticeable unless you're looking for them.