Also, understanding about the "young and green" will help you.
Don't put off the spraying, even if it's not all up yet. Spray it, then spray again when more comes up. When the plant is young and green it's very chemically active. Meaning all sorts of "uptake" is going on at a very fast rate. That makes the systemic kill much more effective.
If you let it get high, and mow it down for ease of spraying, the plant gets tougher. At least I think this is true for Johnsongrass...
"Young and green" will serve you.
Actually there is likely an optimum growth point to spray Johnsongrass for most effective root kill. Let me see if i can find something.
With what you have to do, a little knowledge might go a long way. Stand by.
Here are a couple of links:
The first one is useful even though it's about preservation of natural plant communities, which is not your ultimate purpose. Under "recommended practices" it says, "Best results are obtained when glyphosate is applied to plants that are 18 inches tall to early flowering stage."
Johnsongrass control
This is a good one that will help you understand the godawful plant. This one and the last one give you an integrated approach that will probably be the quickest for you, but some of the stuff in these links may require a license. If you don't have one, farmers around you might help. Nearly everybody is glad to see the stuff gone.
spawn from hell
Another integrated approach