Just use a software solution. Put 6 or or so cameras pointing out radially and then stitch the views together for a full 4pi view. No need for a fancy gyroscope. There's an idea for a startup...
As long as you're going to use a software solution, you might be able to get the number of cameras on the ball down to zero: have a bunch of cameras in the stadium, and reconstruct from them what the ball would be seeing.
(I suspect you'd want the view of wherever the ball was projected to land.)
What about when the ball bounces, or otherwise changes direction suddenly? It would be very hard to watch. But you wouldn't want to make the ball's POV the actual real-time feed anyway, you'd totally lose the context of the game. This technology would only be useful for replays.
Perhaps another approach would be to have a bunch of cameras around the stadium, motion-track the ball in 3d, then stitch the ball's POV together using a process sort of like Google street view, or that dumb 3d revolving-subject thing that was in all the commercials five years ago. Then you could calculate a 'line of best fit' for the ball's trajectory and render video 'just-in-time' for a quick, smooth replay.
