I can't recall ever hearing the name or really even the phrase "Okeechobee Grass" in any of the Florida sings I've been to over the years.

The phrase really now only has an historical connection. Back in the 1930s Lake Okeechobee was diked the whole way around. Prior to this time, the Lake's southern part was really the beginning of the Everglades, hence the "grass." After a particularly destructive hurricane in September 1928 and the growth of Miami and agriculture in south-east Florida, Okeechobee was diked to better collect the water from Central Florida. Canals were dug through what was once Everglades to channel water to Miami and the other cities. The Everglades began to dry up and today only exist in about 50-60% of their traditional area.

I realize that this doesn't help in finding info about the song, but might suggest that it is either quite old (1940s or older) or fairly recent.