Scampi is right from having a supplier that is not certified under a GFSI recognized scheme (i.e. SQF or BRC).
Under BRC, I am required to assure my chemicals (Cleaning Chemicals) are separated from my process. I ensure this by auditing my facility once a month. Additionally, there are requirements on chemicals I use (can be found under BRC 4.8.3).
I highly recommend that you find packaging manufacturers that are certified a GFSI scheme.
I've also worked at facilities that I've certified organic, and found that as long as I have a detailed Supplier Approval program with my requirements, I can ensure this by auditing them frequently.
Unfortunately, most of us don't have time for this, but to satisfy documentation, I would established clear guidelines that your supplier must abide by and have it signed.
Additionally, even have plastic resin pellets contaminated by a chemical residue, the process of extrusion would heat the product above 350oF (dependent on the manufacturer's process). In this case, I looked into my SDS and the flash point of the approved chemicals. Also, any pesticides either have to be stored with a licensed PCO (Pest Control Operator) or in a contained area.
I disagree larger companies do not look into this, because there is too much risk if we contaminate the finished product.
I am only speaking for my company, but with experience at food companies in my past, I've had these situations but was able to find packaging manufacturers that meet these quality expectations we all go through.
Hopefully this would bring some ideas for you to create for your packaging suppliers. Good luck again!