As I wrote above, the camera is used only for the position (FOV [field of view] or orientation is not relevant for VR here), you can even switch to Orthogonal view (front, left, etc), it doesn’t matter for the rendering.
The only thing that you get while rotating the Null (the complete rig—as Donovan suggested correctly) is a preview, if you have the FWD camera active for the editor view in question. For rendering, again, it has no influence. All six cameras are for your inspection of the scene.
The rig has a “Stretched Sphere” attached to it for several reasons, e.g., kind of a safety zone, especially for the equirectagular, as it becomes quite “low-res” where the “poles” are. If you rotate the camera in pan or tilt mode, you lose that prediction, as the “Stretched Sphere” follows (and is so disconnect from the fixed orientation of the VR Renderings).
You can use any camera to do this work, but if you render a [top/bottom] equirectangular out, you have to live with this fixed orientation [in the renderings].
I have tried over the past decade + to create other ways for an equirectangular, e.g., with baking a sphere, but in the moment you want 3D - stereoscopic as well, you have a problem. Even the “white-papers” from Google, don’t get the full problem, but very close. See the PDF
The Key element for any successful panorama is a Lens, nodal point. Since we move our head not around a single eye, nor rotate the head around the center of the eyes, all panoramas produces are kind of a problem anyway. We rotate the head far away from the eyes. In other words all methods that can even produce remotely a good 360ºx180º will fail for this (six camera set up, baked sphere, QTVR, etc. In my photography work for 3D or my art I have shot a huge number of equirectangular images, so I think I have explored it. Check my tutorials about (link is below in my signature)
The impact of the nodal point is less with increasing the distance, hence the “Stretched Sphere”, and its usefulness again.
I have created a little clip, I hope that helps to get closer to solve this. It is one minute long and you can download it.
All the best