Do I have any recourse?
You need to take it higher than the PM. Inspectors need to watch the carrier. I worked as a sub and was questioned by customers frequently about missing items. The regular carrier finally got busted for have truck loads of mail and parcels at his home. The best part was that management had to deliver the items. There have been a few instances that I know of where employees have been caught stealing in my town. We had a supervisor get hauled off by inspectors in front of God and everybody.