Unfortunately, the double insurance won't do you any good because they will only pay for the actual loss, and you will have to produce a receipt to file the claim.
I have a lot of experience with UPS, not very much with FedEx.
UPS can be hit and miss. The horror stories, had a damaged boxed returned with tire tracks on it (was run over by one of their trucks). They asked how I could prove it was their truck? Did not pay claim.
Had a shipment of multiple boxes they picked up. Driver forgot to pick one box up[. They produced a delivery receipt. That is magical since I still had the box in my possession. as trying to prove a point their system was not full proof. They denied the claim and were not amused when I exposed what happened and they NEVER admitted they were wrong.
Whatever you do, don't loose you cool because that will result in a brick wall being built and you will have no chance of collecting.
It is true that once boxes go through the shipping process (being shipped from point "A" top point "B", the box can loose a lot of strength. When boxes are dropped on their corners, the strength of the box is compromised and weakened.
Good luck.

