And the darn stuff lasts for years, underground, making digging and planting a real adventure. The previous owners of our farm had weed block fabric in front of the walkway leading to the front door. Twelve years later I'm still picking up bits and pieces, rags and tatters of that darn fabric! Dichondra, my deepest sympathies. Have you thought of driving by the previous owners new home and shooting out the porch light?
Pull up as much of the weeds as you can...lay down at least one layer of cardboard then cover with cheap dirt and cheap mulch. Leave it alone for at least one year, two is better at least down here....then check to the condition of the card board. It you can dig through it with ease then put down some good soil or compost and start planting. I did that on most of our front yard and now the weeds/grasses are gone leaving behind some very good planting soil,