I do not use chemicals. My wife has an extreme sensitivity, my property is a watershed for a nearby lake, and after attending a forestry seminar on proper application (right time, right chemical, right delivery method) I decided it wasn't worth it.
I did successfully eradicate Tree of Heaven from my forest. It took a lot of persistence and recutting over a period of years. So it can be done.
Looking at the picture. I would weed eat that area down as close as I could get it and then keep watching for shoots to come up. Basic plant biology as I understand it, says there has to be stuff above ground to sustain a root system. If there is nothing above ground the roots have to die eventually. So my thought is that some of the shoots are sneaking up in the tall grass and that is contributing to your problem.
Good luck.
Doug in SW IA