Closing the loop on this. AmEx finally admitted fault and agreed to book them one-way flights home on Lufthansa since BA was sold out. They're currently $6,000 out of pocket for travel costs AmEx has indicated they will likely reimburse them for. They didn't have return flights until 3 days prior to departure at which time AmEx typed the wrong last name on one of the tickets. They called back to get the last name corrected and the flight didn't re-ticket! They almost ended up in the same nightmare scenario as before, but caught it and got it fixed. Extremely stressful and definitely took the wind out of two seasoned travelers sails.