I need more information, as this question triggers many questions.
Let me go quickly and simplified through the problem:
Your description does not tell if it is a VR Sphere, i.e., like a LED Volume that a person can enter, or a sphere that resembles in a smaller size something that the audience can walk around. In other words, is the LED pointing inwards or outwards?
Inwards, the audience can enter.
This would be the 360º camera, which can produce an equirectangular. It would sit in the exact center of the Sphere. OR sit where the eyes of the audience would be, and another position creates some kind of distortion.
However, I believe you want to have not a glass sphere.
Outwards, the audience can walk around it.
This is like a model to VR, or much simpler baking the surface. I have no idea if that would resample your question.
The drop down the Sphere can be really seen without distortion from any point. When it is on the Sphere, it has little distortion; as there is on a sphere, only one point can look perpendicular.
Typically you can build a camera rig in MoGraph, with a target in the center. Then make that editable, which creates all the cameras you need. Those need to go then in Takes to make the process simpler. Then stitched, but also here, anything that is not flat on the surface will create parallax, which will show on the seams.
Not suggested, but for illustration purposes
I suggest using a high-res Sphere with a 100% reflective material (Standard Render) and baking an animation, leaving the Use Camera Vector to influence OFF.
This would be the simplest way
All the best