We used United, which I know is not on your list, however they did lose some boxes and due to the fact that our belongings went into storage for two months while our home was being built there was no way we realized it at the time. We had purchased the insurance but they denied our claim, so our only recourse was to call American Express and submit a claim through them. I was able to recoup my entire loss with American Express.
Lesson here is if you have an American Express card, use that when paying for your move just in case there are any problems down the road. Good luck!
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