I do not mean this to sound rude at all just a general set of questions, so please take no offense. I am trying to help. Why are you swabbing ATP in the first place? Are you actually doing a wet clean? Risk of microbiological issues with food contact packaging should be very low, like almost negligible as there is no scientific evidence of pathogen growth on flexible plastic packaging. What areas are you swabbing? Only food contact rollers and such I would hope. In all honesty you should have been able to risk yourself out of swabbing completely, but now you've started and have failure results so that puts a damper on that. What swabbing technique are you using? Is there a chance you are contaminating the swab by accident and getting these results? Your presses should have dryers that adds a heat source to further reduce any risk and the laminators also operate at very high temperatures, again reducing risk, and another justification. So you should only really swab maybe your slitters. Perhaps that will help?
I've worked in packaging almost 10 years and I have only done swabbing once to prove out my risk assessment and did a pathogen swab with all results negative. It validated my risk assessment and helped to validate our cleaning program as well.
If you are wet cleaning then I would see that you have now introduced a bit of a risk and could possibly justify swabbing. I have only been involved with the SQF scheme, so unfamiliar with BRC code on swabbing for packaging.