I have travelled to Jamaica ON the actual day of Thanksgiving Day a couple of times now. I can't say for sure, now, with the new airline policies of less planes and more crowded planes - but a few years ago, in 2008 and 2010, it was a great travel day. Because it is the only day that whole week when there were very few travellers AND they didn't jack up the fares trying to get people like me to fly that day. The other days usually set records, but not that day. Think about it - everyone else flies the few days before and heads home the few days after.,
As for the short layover in ATL - I would do what you could to avoid it. Since THEY made a change like this, do they allow you to change to go thru, say, Charlotte, Orlando, or even Baltimore (sorry it's been awhile since flown Delta so not sure of connecting cities to MBJ). As others have said, in ATL you will definitely have to change terminals. And if you have the bad luck of both arriving at a gate way out at the end of one terminal, and departing at a gate also at the end of another - it's a long walk/run to/from the center of each terminal (where Ground Transportation is) to catch the Tram/bus/whatever.
If it were me, I would switch to the later flight - getting in to MoBay at 3PM ain't that bad. Who wants that stress if the worse happens. Not to mention Thanksgiving could have snow and delay your initial flight to Miami - getting in even later. Doubtful in Memphis - but who knows where that plane is arriving from.
Best of luck.
