The overall gulf is only mapped as a point rather than an area, so there wouldn’t necessarily be any overlap. It used to be an extremely crude way, but it got simplified down to a node a couple years ago:
Some Wikipedians have noted some ambiguity in the order’s wording: it limits the name to the “U.S. Continental Shelf”, defining its southern limit as “the seaward boundary with Mexico and Cuba”. Under the Submerged Lands Act of 1953, a state’s “seaward boundary” lies only 3 leagues (9 nmi; 10.4 mi; 16.7 km) from the coastline, but I don’t think this necessarily means the country’s seaward boundary is that close to shore, because lots of things can be “seaward”. A plain reading of the order would suggest either the Exclusive Economic Zone or the Outer Continental Shelf designation – which aren’t the same thing.
So until we have more clarity from the feds, any separately mapped Gulf of America feature might also have to be a point rather than an area, to avoid potentially misleading users. That could be somewhat unsatisfying to folks who specialize in mapping the oil rigs and pipelines in that part of the gulf, but it’s not like we have very much certainty about how to map sea limits anyways.