The Mother of All Thorny Things

HELP!
When we moved here 11 years ago, this was a brand new house on a huge pile of sand surrounded by an oak woods. I thought it was beautiful. The builder brought in topsoil (not even enough to call it a veneer) and left us to plant the lawn. It was late autumn so we did nothing for the year. When spring came and we were able to get out and about, we discovered the Evil Plant of Doom - Greenbrier. It was everywhere in our woods, growing up and around every tree, and blocking any passage between the trees. I had never seen it before. Our landscaper knew what it was, but had never seen such a mass of it. She said we had the Mother of All Greenbrier on our little 2 acres, and it branched out from here to populate the state. I believe her. 11 years and I still can't beat it. I'm ready to move. It never did try to grow in the yard where the sandpile and the topsoil veneer is (neither did the grass, but weeds do quite well.) I've been told by local nurseries that Roundup doesn't work on Greenbrier. We can mow some of it, and keep it down *as long as we keep mowing*. But there are so many places we can't mow, and I am overwhelmed.
Our well information shows that they drilled down 50 feet and found sand all the way down. I suspect the nasty little Greenbrier nutlets are growing down there at 50 feet.
I even raised goats for quite a while and let them graze the Greenbrier, but they would only eat little bits of it. They prefer variety and wanted to add the raspberry, blackberry and rose bushes to their diet.
Please someone tell me how to get rid of it.