After brief discussion of your notes we have a few ideas:
Any channels entering the Gulf of Mexico should have created either alluvial planes or scouring on the bottom of the Gulf.
If the level of the Gulf was maintained for an extended period of time then evidence should exist to verify it. Possible evidence would include layers of salt and/or fresh water organisms.
Drilling cores would be possible source of evidence.
One guy thinks he has some evidence of this scouring, don't know the details. I agree that some core samples would/could/should clear this up fairly easily. I was also thinking that a reduced water level Gulf would have increased salinity, boating would be much easier, huh?