But here's the trick. Now, I will preface my remarks by telling you that I have not personally gotten rid of dogbane, but then I don't have it. But I used to write a gardening newsletter and on one occasion, I discussed another similar type weed and I think the protocol would be the same. The article was based on my personal experience.
First, dig out what you can. Then cover the ground with cardboard and a heavy mulch cover (5 inches, no less). I used leaves.
After that, you make an every 3-days investigation to see if it broke through your mulch layer. Start this procedure about 10 days after you lay down your mulch cover.
If it does, you simply dig it up again and replace the mulch cover with more cardboard and another layer of mulch.
This really is not an onerous treatment plan. I got rid of my nemesis relatively easy, and mine was an underground spreader that would root 9' deep.
The key is the diligence. Just make it a priority to go after it when it rears its ugly head, and you will win out.
Cher