Scenario B: Walmart rents a $5 digital ocean VPS and installs postgres. Each producer generates a (e.g. GPG) key pair and sends the public key to Walmart. Each day, each producer creates a new entry in the db, signs it with his/her private key, and is done.

The mining is completely worthless in the scenario you described. Imagine either a rogue producer or Walmart having an interest in changing the database. In your scenario of 10 mining boxes the adversary would just have to buy 5 additional boxes and would have complete control over the blockchain.