The reason horseradish is so difficult to eradicate once deeply established is that it grows well from root cuttings. If you dig out a very large parsnip and leave a small amount of root broken off, it will die and not be a problem. If you do the same to a horseradish plant, it will regenerate from the broken root. Because of this, it is a good idea to restrict its root growth. Have you seen if anybody else has horseradish at your plot who will let you have either a plant or a piece of root? Either will establish quickly in my esperience in ordinary garden soil. You can grow horseradish from seed but most suppliers only supply root cuttings which they call thongs.