I've actually never heard of the phrase before (though I lived 10 miles from the Lake in the 80s and am an historian and folk-music junkie in Central Florida currently. I've never seen it listed on a map either.
I am assuming that it is related to the info I provided. I doubt that it was ever used for a name for the Everglades. The lake was a pretty definate body of water, even before the dike, the water just percolated over and through the sand and soil in the southern end. That part directly south of the lake could be referred to as Okeechobee grass, but the Everglades is such a huge area. The Everglades used to extend up both sides of the lake and out towards both coasts. An area probably 3 times as large as the national park. Then there's Big Cypress Swamp - which is part of the Everglades as well, in general, but it's a basin of sorts and the water tends to be higher as in a regular swamp. The Everglades themselves is actually a unique geographical feature. There is nothing quite like them anywhere else in the world. They are somewhat similar to a broad river delta, but there are many differences.
Is the tune just music or does it have lyrics? Can you share any more info? I can ask around with Florida folkies.