Did some investigation years ago because in my part of AR we also have a lot of Sweet Gum trees. There are some sprays that can be used to help, but with the size of most trees you would have to have a pretty good spraying system to be able to apply the material and have it do any good. One neighbor cut down the last of his (yeah!!), and another one bought a sweet gum ball "picker-upper" that he pushes around and it has flexible fingers that grab the balls and dumps them in a hopper. Actually it works pretty good (cost about $350). I've got one 85-95 ft tree left with 2 trunks that I hope just dies and falls apart a little at a time. Too big for me to cut down in it's current location without taking out a mortgage on the property to have a tree service come out and do it for me. Other than that, I just run my mower over them and cut them up. I have a mulching deck and keep the blades sharp; don't side discharge cuz them little buggers really come whizzin' out.