Snap is a bad word to describe the movement but since you are using it:
So what happens when that heel angle is reached? Does the fin keel boat just sit there, frozen in time?
No, the boat will snap back almost as fast as it snap before on the opposite direction. When the light boat is already "snapped" back, the heavier boat is probably still rolling down slowly or perhaps it is starting slowly to come back to its feet.
Still waiting for the damping explanation......