Send identified packed examples of the actual seam, print and board conditions. Ask the supplier to assess the full handling movement and loss-of-hold response, not just lifting their clean sample.
Price that preparation as part of the method. If the packer must sort and turn each carton, the handling demonstration needs to begin before that work. Otherwise you are comparing a ready carton with the job you actually receive
Then include correcting the label orientation at the receiving end. Your trial should count both people's work, and ask them whether the new handling is actually easier, not only time the robot's movement.
We tried the proposed preparation with both packers. More handling at both ends, no useful relief. We stopped this purchase proposal. Thanks Julia; the receiving job was missing from my comparison.