[HO455]

Are the pictures from the first incident or the second time? I would look very hard at the oiling system. Inspect the oil pump and its relief valve. Pull the filter and cut it apart to see if it is plugged. Check the filter bypass. Pull the galley plugs and rod the passages if necessary.
Low oil volume will cause the valve train to overheat. The oil that flows from the push rods down over the rocker arms valve springs and the down to the valve guide is what cools those components. If the volume of oil is not enough then heat builds up. The heat causes the guide clearances get tighter which in turn makes more heat. Worse case is the valve siezes and it is hit by the piston.
The gauling on the push rods in the photo look to me to be oil related.