Unity Simulate Local Rotation

I've run into a situation where I need to be able to use a relative Y rotation for my player. This is so the player can walk on walls, floors, and ceilings and operate "the same way" regardless of actual rotation (I've already got gravity and such sorted out). The game in which I'll be using this is an FPS if that info is relevant.

I came across this: http://answers.unity3d.com/questions/518399/simulate-child-parent-relationship.html

But it doesn't quite apply to what I'm trying to accomplish.

This is my present code for turning the player, but it isn't suited for different orientations (it successfully works between a floor or ceiling for obvious reasons though).

  angle = new Vector3(_yMouseAxisLocked ? transform.localEulerAngles.x : currentYPos += yCoord,
  xMouseAxisLocked ? transform.localEulerAngles.y : currentXPos += xCoord,
 transform.localEulerAngles.z);
 transform.localRotation = Quaternion.Euler(angle);

Ideally, I'd be able to pass the resulting Vector3 in the above code into a method that does the work of figuring out what value each axis should be set to based on the players current orientation.

Something like:

     Quaternion RelativeRotation (Quaternion baseRotation, Quaternion relativeRotation){
        // Do math
        // return final result
     }

My usage of the method would look something like

  angle = new Vector3(_yMouseAxisLocked ? transform.localEulerAngles.x : currentYPos += yCoord,
  xMouseAxisLocked ? transform.localEulerAngles.y : currentXPos += xCoord,
 transform.localEulerAngles.z);
 transform.localRotation = RelativeRotation(Quaternion.Euler(_rotation), Quaternion.Euler(angle));

Its been quite a puzzle trying to find anybody in the same boat as me. I'll admit I'm not math savvy or that knowledgable when it comes to Quaternions.

This image should clarify the application of this.

Note: Take no mind to my present code using local rotation. The script this is from runs on game objects with parents, and game objects without parents. A check will be added to determine if the game object has a parent or not.

Edit:

Started toying with the following code. Only partially works when on walls, If I look at a veiwing angle greater than 45 degrees either direction the player starts spinning out of control.

     if (isOutsideGameObject) {
     angle = new Vector3(_yMouseAxisLocked ? transform.localEulerAngles.x : currentYPos += yCoord,
                          _xMouseAxisLocked ? transform.localEulerAngles.y : currentXPos -= xCoord,
                          transform.localEulerAngles.z);
                          Quaternion startParentRotationQ = Quaternion.Euler(new Vector3(
     !_yMouseAxisLocked ? angle.x : 0, !_xMouseAxisLocked ? angle.y : 0, 0));
                              transform.rotation = (Quaternion.Euler(player._rotation) 
 * Quaternion.Inverse(startParentRotationQ)) 
     * startChildRotationQ;
             } else {
             angle = new Vector3(_yMouseAxisLocked ? transform.localEulerAngles.x : currentYPos += yCoord,
                                _xMouseAxisLocked ? transform.localEulerAngles.y : currentXPos += xCoord,
                                transform.localEulerAngles.z);
                                 transform.localRotation = Quaternion.Euler(angle);
             }