Both Barbados and US has ratified the Montreal Protocol, thus the Montreal limits apply (1000 SDR max liability for luggage, approx USD 1500). If it were a trip within the US 50 states, the AA limit would be USD 3000, but excludes:

- No liability for photographic equipment, computers, VCRs and any other electronic equipment including software or components, jewelry, cash, documents, furs, works of art or other similar valuable items

The Montreal Protocol has fewer exclusions and might cover more items for the OP.

In most cases of theft, the bag is delivered either on-time or within a day; just missing a few items. It is rare to have the entire bag stolen -- the baggage sorting areas at most airports are covered by CCTV and have other anti-theft precautions. Much easier to pocket an item than a whole bag. JFK did have a major theft ring which included dozens of baggage handlers, but this was broken up several years ago and most are now in jail. Chances are your bag had a damaged tag, got misrouted to another airport (e.g. Bahamas instead of Barbados), lost its tag and is now languishing on the ground at some strange airport, never to be seen again.

The FT standard is to presume checked bags will never arrive, and pack accodingly. Thus the almost maniacal focus on carryon bags and the various limits around the world. Fwiw, I've done RTW trips with both summer/winter seasons, lasting a month, with only carry-on (but it did require buying special clothes and careful packing). AA seems to be better than average at getting bags delivered, but has very poor communication about what is happening. There is still some chance that the bag will be found, but at this point the normal recovery techniques have failed (all bags matching yours have been checked for tags and internal name/address labeling, etc.).