Aye Mate,
Try the Brunnings product, usually from BigW or Mitre 10.
It was marketed as "RESOLVA" in Bunnings, but did not sell too well.
It is the best foliage killer I have used, completely different consistency to Round Up and Zero.
Should be a greyish claggy type of mixture!
It seems to stick to the plant for longer and as the blurb says, results are seem in 24 hours.
I reckon, if you mow the "Nut Grass" and apply this stuff immediately after, you will win the war.
Wayno