I was also thinking of attaching a 3" piece of trim to the sides of the cabinet that would stand out parallel to the door.
Some have luck with bicycle inner tubes
Weather stripping is another choice. Perhaps a frame of furring strips inside the door. Greater surface area to attach tubing or weather stripping plus, it forces the light to bend twice at 90º and light doesn't like to bend.
could try thick metal tape with a strip of paper left on it where the hinge would touch