I also operate a DTC company and ship similar volume.

8 years ago, when we started, we shipped exclusively in tubes. The loss rate with USPS was somewhere between 5-10%, it was too painful to measure exactly. I switched to a custom-sized "ear lock mailer" rectangular style box, and lost rates dropped below 1%.

My theory was that the cylinder shape was rolling off of some sorting line / conveyor, or possibly the tubes required a different (maybe manual) scan that had a much higher failure rate.

So I don't ship in tubes with USPS anymore (UPS and FedEx don't have same issue).