Answer: What you propose is a good idea! If you can exclude light, the shoots any remaining ivy roots produce will quickly die. I'd use a combination of newspapers and a spun fabric weed barrier rather than black plastic. This will allow water to penetrate, but not sunlight. I'd leave the weed barrier in place indefinitely (or at least until it weathers away). Eventually you'll get the upper hand over that ivy - don't give up!
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