My guess is that two of the three screws have been gone and the third one finally loosened enough for the flywheel cover to come uncentered and sling around. That off-balance weight is what caused the severe vibration and chewed the foam air seal to pieces, and then gave the flywheel cover room to lift, and the last screw let go. The top of the engine cover is scoured by the cover spinning around. Does the engine run smoothly with the cover off?
That foam ring should be replaced, it seals the top of the engine when the hood is down so it will pull cooling air from outside the hood, which is much cooler than the heated space under the hood. Most JD models of the late 90's through mid 2000's are made that way, my 2002 GT235 is the same design.