We also discovered patches of PI after buying our house. The main patches were in big areas of rock outcroppings. We suited up with long garments, wore gloves, masks, and taped bags around our feet and pant legs. We removed four truck loads of the stuff by hand. The next day I was fine . . . DH was not. He was one big blister from head to toe. Not a singe spot, NONE, was not affected. He became feverish and had to see the doctor.
I decided to go ahead and remove the rest by myself. Suited up as before. This time I did end up with some on my mid section. It was pretty bad and I got medication as well.
What we learned about it was that it sends runners underground for many, many feet. If you don't pull up all of the runners it just comes right back up. Of course, being in rocks were not going to be able to remove it all. We've sprayed with "Round-Up" and other products but it comes back. Luckily it doesn't take over the yard. Every once in a while my DH will get a small patch, brought in by one of the dogs. It is very dangerous to burn as mentioned by another poster.
There are people not affect at all by PI. You could advertise and see if they could come clear around the house at least. As far as the rest of the property I think goats are your best bet. I'm sorry it wasn't disclosed. We bought our house in June. It was beautiful, the previous owner had some lovely deck furniture and potted plants on the deck. What a view!!! Well, come October, the winds started whipping up and from October through May it blows like a hurricane. I now know that the "set-up" on the deck was for intended for "flatlanders" like us.