In my general experience with AA - 4 hours is the earliest you can check bags at the kiosk.

I had this issue at LAX earlier in the year where I had to wait a little to get under the 4 hour mark.

At EYW you don't really need to be there early and arriving 60 minutes before your flight is plenty. Just be mindful of the 45 minute baggage check in cut off if you don't have any luck getting the ticket agents to let you check your bag for the return sector when you arrive.