Digging it up is a chore but can go a long way to erradicating it. You will have to follow up with more digging later as you won't get it all. I think the idea of smothering it with a mulch cover will work if left on for a longer time. I would use a landscape fabric weed barrier as it allows air and water to pass through. After 6 months to a year the plants beneath the cover should be pretty much gone.
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