Again, I think this could be solved by giving the customer the option. Single box is free, double box we pay the delta in cost.
Please don't take this the wrong way, but it's really up to the shipper to make sure the package is packed in a way that it does not receive damage in transit. If this means passing the the cost on to the consumer so be it.
Personally, if I had an option to select additional packing at my expense at checkout even though Axiom told me that the package was fully insured, I would not pay for it.
I sell products on eBay that range from $50.00 to over $500.00 and do my own shipping as well. I could not see me asking a customer if they wanted to spend a little extra, just as a precaution to ensure that the product they are receiving will be safe. It's my full responsibility as a shipper