St. Augustine

St. Augustine is probably one of those life forms along with cockroaches that are sturdy enough to survive a nuclear war.
I am taking out an 'L' shaped strip of Augustine about 4' x 100' (in order to put in roses and wildflowers and zinnias) and I've been working on it for weeks.
The strip got sprayed twice with Roundup two weeks apart. I thought when the top was nice and brown and dead looking, I had it made.
Wrong.
I am having to go through the top of the dead lawn one foot at a time and pull up the still green underground runners. It is like the Borg, the entire yard seems to be connected. So that's 400 square feet I'm going through, foot by foot. The runners have roots every few inches so I can't rent a dethatcher, because that might leave a bunch of rooted bits in the soil.