Keep escalating until you get to the independent review. Ask them to check GPS coordinates to confirm the postman was at your house. Not sure how often they refresh location but this could prove they were at your door for more than a minute? (Long enough to collect parcels)

Ask them what evidence they expect to see. It is not your job to scan the items and you cannot control what the postman does.

If you have printed your labels and have purchase receipts for the items that are no longer in your possession then they have to investigate it fully.

Keep at them and be persistent.

I was fighting with them for 2 months for an item which got lost which was worth £5. The loss didn't bother me, but it's the principle. Companies get away with so much nowadays. In the end I got a £20 cheque for the inconvenience.