Creating just a non-stereoscopic 360 capture setup is highly difficult, unless you are shooting vast landscapes with wide angle lenses.
The problems you will need to factor are far more than overlap.
Yes, you will need adequate overlap for adjustment in post production. But you also need to make sure all of the cameras are genlocked for sync. Shutter speeds will need to match, as will white balance and f-stops.
If you plan on having objects come near the camera (which would be why you'd want 3D), you will need more cameras; because for 360 you want to use high quality lenses in the mid to wide focal lengths.
Your issues will be focus, and mostly, warping as the objects move closer to the camera. Once in post, the objects, unless you are (factoring full frame plane of view) using 50mm or longer lenses, will distort due to simple physics. And will be near impossible to align in post-- especially so with a steroscopic rig.
Im honestly trying to envision your setup, and would think in order for anything like this to work, your camera ring would need to be fairly large; like 6 feet in diameter. Using 16 or more pairs (32 cameras) at the very least. Anything less will not produce appealing results.
The few 360 setups I have seen in person used 22.5 degree slices (16 cameras and 16 projectors).
Hope this helps.