My memory is a bit foggy because this legislation really ramped up about 15 years ago. There was a lot of money thrown at this from both sides. A lot of big non-profits really wanted that ban and the Lacey Act amendment banning large snakes put into place, and they spent millions to make it happen. There were a lot of studies being done around that time, but to my knowledge none of them sufficiently proved measurable impacts to the environment, especially not outside the limited area in FL where it's an issue. There was a big study done, I think it was in NC, where they were trying to figure out just how far North Burms could survive, and none of them made it through the winter, but somehow they still used the study to push for the ban. I'd go the route of searching up the big snake ban Lacey Act, even though you are specifically asking about FL, because there is a lot of overlap in what was used to push for both.
It's my opinion, but I don't think the legislation has helped slow or reverse the problem at all. The fact that Burms were able to establish a wild population in the first place, it's going to be near impossible to eradicate them, but a lot of passionate people in FL go out and hunt them to try and keep the numbers in check, and I think that has had a much bigger impact keeping them in check than the laws have.