I'd suggest writing up your own receipt, with the person responsible for your bag. Make a list, and each of you can sign and date it. If they offer the service of holding your bag while you shop, they assume some limited liability for theft or damage. If that doesn't work, freeze something horrifically gooey and rotten, put it in a bag you don't love anymore, and leave it with the manager quick: before it thaws. After this, when the manager starts demanding to dig through bags, have some legal help remind him that this is illegal. The police might play along, or maybe even the local news.
If the store manager can't come up with a reasonable system, he's wide open to all sorts of mischief.