It's a little incredible what lengths filmmakers will go to get all possible perspectives in a certain situations, but sometimes that's exactly what the situation calls for. You could buy way too many cameras or waste money on an unsure deal, or you could perhaps turn to a dedicated broker for used professional video equipment that might solve your problem in one swoop.
This includes the issue of panoramic recording, or taking in multiple angles of one thing. You might risk too much by going out on a limb to find the answer to this situation by pursuing strange contraptions.
Videomaker recently devoted a post to a strange-sounding project called the Panono, a ball with no fewer than 36 cameras in side that one can presumably roll around a scene and capture all of the details inside.
Perhaps we should say "will presumably use," because this is only an item in development that's still looking for funding, and not something production companies can seek out to buy right now— another reason to be skeptical about whether this will be a reliable product.
So let's focus instead on something currently available that does work. New Pro Video Systems can point interested buyers to the Skyjib 8 Octocopter, compatible with RED cameras and useful for anyone who needs a bird's eye view but can't afford a helicopter (or a bird, for that matter).
Once you have purchased used professional camcorders that fit your needs, you might naturally start thinking about ways to use it, and this device could help answer your production questions and make for a general increase in efficiency.