I always use UPS when shipping a quilt, or anything expensive. The first $100 of insurance is free and the rates are cheaper than USPS, usually. Their tracking is excellent. USPS tracking has gotten better in recent years, however. And UPS is very good about paying out claims. If it is less than $100 or so, they just pay, they don't ask to see it or anything.
One time I did have a problem with UPS, I sent something next day air and it got stuck in my state. When I called them, they refunded my money and sent it Next day air Early AM at no cost!! Try to get the PO to do that!