Disney's Resort Airline Check-In (RAC) will check in as many bags as you have to the airport. You are not limited to one per passenger. If the airline has a fee for more than one bag per passenger, then that fee will be collected, but RAC will still send the bags on. As you mention, Southwest Airlines allows 2 free check-in bags per person, so there will be no fee for those if you're flying SWA.
Magical Express will take as many bags as you have from the airport to the resort for you.