How can I access negative rotation data or is there another solution?
What does that even mean? 
What I’m trying to say is why can’t we access the negative or direct data written in the inspector panel in Unity?
Because those numbers aren’t real. The XYZ Euler angles displayed in the inspector are simplifications for the purpose of quick adjustments in a human readable format. If you need more accurate rotation manipulation, that’s what Quaternions are for.
Oh boy, you are in for bit of a headache.
This article explains most of why Unity has Euler angles as well as Quaternions: Game Dev: Unity — What are Quaternions and Euler Angles? | by Ethan Martin | Dev Genius
You don’t need to understand it accurately right away. Most things can be done without ever truly seing a quaternion due to the useful libraries Unity brings.
Best if you tell us what you wish to achieve 
To add to the above, if you want to actually maintain a rotation value that can be positive/negative, you should maintain that value yourself in a custom monobehaviour, then generate the final quaternion rotation to apply the transform with said value.