I think it's much simpler than that. Instead of factories self-reporting, you have rivals report on each other, as well as client and suppliers report on what went in and out of the factory in a given time period.
It wouldn't be a perfect system, but like capitalism the competition would force everyone into relative honesty. It is pretty weird they didn't do that at the time though, considering the KGB kinda had that sort of setup with respect to everyone individually being required to snitch on each other.
Workable at tiny scale in religious communes, or maybe for a different species.