In my area... Nutsedge grows right through those ground fabrics.
Suggest finding some old wall to wall short fiber (not shag!), lay over ground pile side down.
That carpet works a treat for most of these applications.
Of course... I have heard of a chem called brand name sedgehammer... For those people brave enough to use that kind of dangerous stuff when the tv is so full of lawyer ads about those nasty herbicides...
Choke out the existing vegetation?
Not gonna happen.
Worse... Planting that kind of aggressive stuff is always worse than the original problem...
Like they say about ass deep in alligators...
Those aggressive plants that you purchase to crowd out the existing vegetation always escape and destroy the surrounding countryside.