I would have to observe the process from raw material to shipping dock to be certain, but my past experience tells me there are several options to mistake proof the process of labeling. First, and foremost, of course, is to understand the problem is with the process, NOT WITH THE INDIVIDUAL APPLYING THE LABEL! (the comment "Recently we had another issue where she switched up the packing slip documents between two other shipments." means the company is aiming at the employee, NOT the process.")
NOTE the sample label mentioned does not seem to be attached.
I presume, from the OP description, the REAL packaging of product is done in flexible plastic bags which are then inserted in sturdy plastic cartons to protect them from damage during shipping and storage. It appears that labels need to be affixed to the plastic bags first, then to the outer container.
POSSIBLE ROUTE TO CONSIDER:
Sometimes, management and employees are so indoctrinated into a current system they simply can't envision another process to incorporate mistake proofing measures. In such cases, it may be worthwhile to bring in an "expert from afar" to look at the process with new eyes. There are a number of sources of such experts ranging from independent consultants to label company staffers who can provide this expertise.