Kill St. Augustine in Fescue (marathon lawn)

I'm in LA. I have St.Augustine in my fescue I'd like to get rid of.
My local garden center recommended this http://www.montereylawngarden.com/pdf/turflon.pdf
Another said no chemical exists. Anyone have any opinions ?
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The St. Augustine is a couple long strands that are much higher than my fescue.
What if I got a rag and smudged Roundup. Would getting roundup on the top inch or two of the grass kill the root ?
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