chickweed: my 'mother of all weed battles'

[Agamemnon]

I am having the mother of all battles with some chickweed in my backyard, next to my pool. It's taken over about 2/3 of the yard. I tried a hose attached broadleaf weed & feed and recently tried a granular weed & feed. It's almost as if the chickweed is eating it with the sole purpose of pissing me off.

Anyone have any recommendations for treating, killing this **** without killing off the St. Augustine that is struggling to live under the chickweed alien pods?