You're in the islands, man! Competence is a sometimes thing, but laughing and joking are an always thing. If you don't get home today, you'll get home tomorrow...or sometime.
AA would reimburse you for the hotel if the delay were their fault. The airport being closed isn't their fault. You could take the position that if you had known earlier, there might have been same-day space available out of SXM. The problem is that you don't know that, you just know there wasn't anything by the time you called. You might get something, but I don't think there is an entitlement to it.
The cab fare and ferry fare you might get. If AA had rerouted you without you asking, you would definitely be owed these amounts, but they rerouted you because you asked (perhaps demanded). More of a grey area.