Why does it seem obvious to use poison?
At my house, cutting the tree down, and cutting the sprouts off with an axe after they get large enough to bother with is generally enough.
If necessary, cut any returns.
The secret is to let the tree stump get invested enough in the new sprouts, that cutting them once exhausts the roots.
I can put in vegetables after this action. Matter of fact, I am putting in vegetables in what was a grove of trees last year at this time. No grinding, no poisons, nothing to it.