I wrote a short paper a couple of years ago about depositional patterns along the Sigbee Escarpement (on your map, it is the underwater "ridge" seen in the north part of the remaining Gulf of Mexico. I interpreted quite a bit of 3-D seismic as part of the project. On the shelf, the stratigraphy is very complex, and unconformity-bounded sequences are plentiful. Even in the area of the deepwater Gulf of Mexico that presumably has never been completely dry, the lack of well control complicates the interpretation. From what I have seen, I have doubts about "sea levels" being much more than 500 feet below present day sea level in the past 2 million years. There have been several glacials and interglacials during that time, and sea level has fluctuated significantly. I would be interested to read the articles that suggest archeological sites at 2000 feet below present sea level.