I grew up in Memphis, where sweet gum trees are quite common. I hated the balls, especially stepping on them! The common remedy was to rake them with the stiff leaf rake, yes, a real pain! I wonder if a good blower would work to move them into a concentrated area, then rake up?
Fast forward to now, I'm SW Ohio and, though not as common, I see some sweet gum trees. And always comment on the mess of balls under them. I recently mentioned to my wife that I was thinking about planting one on an outer edge of our property, where the balls could fall and remain. I do think the trees are nice looking. Might be a crazy idea....
I have several Osage Orange trees around the outer areas. Some years I pick up literally hundreds of hedge apples, last year maybe 30. I did have 20+ trees removed when we first bought the place, no regrets there! Walnut trees have similar cycles with the walnuts.
Best of luck,
David