If you can get ahold of a huge load of wood chips (call some local tree guys), throw about 6" layer chips on top of the fabric over that entire area. Wait a year, pull up the fabric, rake everything flat and then do it again. Literally the only way to kill the stuff is snuff it out longer term. Looks like you've got a good start! GL~!
Discussion
Yeah I did that with the garden area because it was taking over. This coming fall/winter I’m going to run the chickens over the area to scratch it all out. I’ll let them do the hard work.