When I stayed there a while ago, service and some rooms were bad.

Ask for a late check out. Some hotels will give this for free if they're not too busy, while others charge a fee, often $50 or half of a day's rate to 4 or 6 pm. Most hotels have some way for you to continue to use the pool, spa, and other facilities after checkout.

If your meeting is at Planet Hollywood, it would also be natural to leave the bag there, perhaps hanging out to work in their lobby/public space or outdoor garden, although normally you can't use the pool unless they allow the general public to do so for a fee.

If you can manage with just carry on, you could go to the AmEx lounge as early as you want,, assuming that you can do OLCI to get through TSA security. You could even take a "carry on" bag with you to the lounge and then to land side at T-4 to check the bag with AA if you don't want to actually carry it on board. Some airlines will also gate check bags upon request, but I'm not sure about AA if there's enough bin space on the flight.