OP: Sorry you had a lengthy delay. I concur with others you got a surprisingly generous and accurate compensation offer without having to do much effort to get it. TAKE IT.
You leaving out the reply and the offer of compensation in your original post was significantly misleading to your situation you described. Instead you translated a generous cash offer into "woe is me" and complaining about corporate America. I realize it really wouldn't have been as impressive if you'd shared that up front, but you should have,
Meanwhile, think about your situation: you were travelling on Dec 22. 3 days later is christmas. AA offers you creative ways to get you close to home, and eventually all the way home, and you turn up your nose? At the busiest travel time all year? And complain about the 3rd party shuttle company not having someone at their desk that AA should have been on top of that? I'd have pushed my 92 yr old myself, pacemaker and all, to try and get home if I was travelling for the holidays. 2AM or not. You come across as being kinda picky in the way you wrote this, but I doubt you meant to sound that way.
Regarding "the airport was open" What your family members or tv crews report doesn't mean the airline can make it happen operationally. THey may have cancelled that plane and reassigned it to replace someone else's mechanical problem, or whatever, and now that the airport seems available again, it's too late to put the flight back on. It's just a logistics issue. I would take the media or a family member saying "it's dry here" with a grain of salt.
Hope your travel next Christmas is better. You can take 4 more trips for 2 with the money you made.