Is the Hajj considered valid, and is expiation (kaffarah) required, for someone who was unable to spend the night in Muzdalifah on the Night of Sacrifice within its boundaries due to severe overcrowding, and thus spent the night near it?

Your Hajj is valid. Staying overnight in Muzdalifah is an obligation, not a pillar. Whoever neglects it must offer a sacrifice (dam). However, if one neglected it due to the unavailability of a place or being prevented by soldiers, then there is no penalty. But if it was neglected out of negligence, then a sacrifice (dam) is due, along with repentance.