Quads snapping up or down when displacement is animated

I am trying to make a 80’s style grid mountain valley animation with the scene slightly animated by a noise texture displacement.

However when some deformed faces cross a certain point they “snap” either up or down creating a very distracting and bad looking effect.

I have made the initial mountains by applying a noise texture to a plain and modifying it to create a valley path for the camera which resulted in some faces being distorted or “bent” by having two opposing vertices below the other ones, this creates a jumping or snapping effect when the displacement makes the geometry cross the threshold of the “bend” being in the opposite direction.

Is there any way i can fix this? Like, disabling the snapping, or making it always face one direction without manually readjusting 150k+ faces?