Wow, that is indeed a conundrum. From what it sounds like, you are probably right. I wonder if you could try putting a silica pack in the middle of one of the rolls before it makes the trip to see if that absorbs anything. Like they use for food to reduce moisture etc. Does the damage to the tube reduce the effectiveness of the shrink wrap? Are you just concerned that it doesn't look very good to your customers? I guess that would be another thing I would consider. Is it just optics or is it impacting the performance.
Been doing some investigating today and it looks like the tubes need 4 days to cure to reach their core strength. This is obviously not happening currently and the factory needs to wait a little longer before production and order differently to what they are currently used to. The problem occurred when I came on board with some big customers. Just shocked I had to find it out and not the cardboard manufacturer.
Glad you are getting to the bottom of it!