I mowed Johnson Grass in late Summer, then I sprayed the regrowth with glyphosate using a boom sprayer, and then I burned it in the Winter. The following Spring I sprayed regrowth with Gly using a boom sprayer. Prior to planting, Johnson Grass came back again! Determined to win the war, I sprayed Johnson Grass with Gly every time is came up all Summer, thinking I'd eventually deplete the rhizomes, and toward the end of that Summer I sprayed two applications of the grass selective, Poast Plus.
The following Spring Johnson Grass came back with a vengeance, because I'd eliminated the competition. I've since learned that Spraying Glyphosate is akin to seeding Johnson Grass. I had a friend on another forum who was a Monsanto Engineer and he worked with me to change the Glyphosate mix, thinking a slower kill might be taken further into the rhizomes... nothing worked!
Plateau kills Johnson Grass, and has a residual effect, but one Johnson Grass plant can produce 50,000 seeds that last ten years in the seedbank. When established Johnson Grass is sprayed it can come back from seed, rhizomes or a combination of the two, since seed will remain viable in the soil for ten years!
Johnson Grass can be shaded out, or it can be controlled by grazing and haying, and I've seen corn successfully grown, and also beans.