You can do advance check-in, and leave luggage at the baggage area to the right of the FW "lobby / front desk" area (having a major senior moment, so can't think of the appropriate wildernessy name). You will need to make advance (per phone) arrangements to pay airline baggage fees for remote baggage check, and have that confirmation number available when you check your bags. They can also issue your boarding passes provided you have confirmed seats for your flight(s).
I don't know about leaving your carry-on, probably best to inquire, but I'm guessing this would be a function of the front desk since the baggage check-in area is manned from early AM until only about noonish. Nobody is there if you are actually departing FW later than early PM so I don't see how they could retrieve your carry on.
A word of caution: I got various, usually wrong, answers to inquiries about all of this from the front desk or by WDW phone regarding baggage checking: example of some RIGHT answers - you do NOT have to be using Magical Express transportation to the airport in order to check bags. You DO have to be flying on a participating airline.