I think the limitation is USD1400 on an AA international trip. I haven't checked, but it may be that AA has an additional requirement that jewelery is not put in the hold, which may mean they won't pay for this, or try not to. It's really unfortunate since AA usually are pretty good at finding lost luggage, but I think you better work with Amex amd AA to come up with a negotiated outcome. I doubt that sentimental value will get very far here, I regret to say. It will be down to a strict valuation of the items concerned. It's quite normal for airlines to insist on receipts, but equally normally to push back to say they are no longer available. However some credit card companies are willing to pull out transaction data if you are able to narrow down the dates and vendors concerned.

The other things that really should not be put in the hold - purely from a value recovery point of view - are electronics, bank notes, share certificates, bullion and other valuables such as paintings and antique clothing.