Camera matrix shifting is moving my skydome

Dear community,

I'm using a script on my camera that moves the projectionMatrix so my perspective changes with the player moving in front of a big screen. I've simplified the script so only the matrix bit is still there instead of boring you with the details.

The problem is that my world reacts normally to the matrix shift, but my skydome moves along with the camera. This results in a weird effect. I've tried to put a skybox on a sphere and that works fine. I've got all my lighting setup and don't feel like making a new scene if any of you know a fix.

I feel like the problem is in the skydome script, but I don't have much knowledge about the shader scripting, apart form culling and lighting.

 public var cameraPerspectiveAmount : float = 0.3;
 public var range : float;
 public var myCamera : Camera;
 
 
 function Awake () {
 
 }
 
 function Update(){
 
                 
     var xPos : float = Input.GetAxis("Horizontal");
     
     SetVanishingPoint(camera.main, Vector2(xPos * cameraPerspectiveAmount, 0.0));
     transform.localPosition.x = xPos * range;  
    
    }
 
 function SetVanishingPoint (cam : Camera, perspectiveOffset : Vector2) {
     var m = cam.projectionMatrix;
     var w = 2*cam.nearClipPlane/m.m00;
     var h = 2*cam.nearClipPlane/m.m11;
  
     var left = -w/2 - perspectiveOffset.x;
     var right = left+w;
     var bottom = -h/2 - perspectiveOffset.y;
     var top = bottom+h;
  
     cam.projectionMatrix = PerspectiveOffCenter(left, right, bottom, top, cam.nearClipPlane, cam.farClipPlane);
 }
  
 static function PerspectiveOffCenter (
     left : float, right : float,
     bottom : float, top : float,
     near : float, far : float ) : Matrix4x4
 {
     var x =  (2.0 * near)        / (right - left);
     var y =  (2.0 * near)        / (top - bottom);
     var a =  (right + left)        / (right - left);
     var b =  (top + bottom)        / (top - bottom);
     var c = -(far + near)        / (far - near);
     var d = -(2.0 * far * near) / (far - near);
     var e = -1.0;
  
     var m : Matrix4x4;
     m[0,0] =   x;  m[0,1] = 0.0;  m[0,2] = a;   m[0,3] = 0.0;
     m[1,0] = 0.0;  m[1,1] =   y;  m[1,2] = b;   m[1,3] = 0.0;
     m[2,0] = 0.0;  m[2,1] = 0.0;  m[2,2] = c;   m[2,3] =   d;
     m[3,0] = 0.0;  m[3,1] = 0.0;  m[3,2] = e;   m[3,3] = 0.0;
     return m;
 }

Thank you for helping out!