I've seen smart weed growing very heavy, almost a mono-culture in some field lanes, areas where the vegetation overall is kept mowed pretty short. And the soil is compacted by the vehicle (tractors, pickup truck, 4 wheeler.)
And right next to this is often a field with a good stand of grasses & legumes. And in there you see little or no smartweed.
Why the difference? Part of it I think is the compaction of the soil. That seems to favor smartweed. This is not something I've read. It's just a pattern that I think is true, from my own observations.
If it's true that compaction is favorable for smartweed and not so good for other plants that when thriving crowd out smartweed, that might give you some ideas to try.
That is, loosening up the soil, then seeding with something else that hopefully will crowd it out. Maybe a grasses/legume mix?
Let us know what happens.