Answer: Unfortunately, goutweed spreads by underground runners as well as by seed and is extremely difficult to get rid of once introduced into a garden. In my experience it is better to remove (and either discard or scrupulously clean the desirable plants to avoid replanting even a shred of goutweed root) and then resort to drastic measures to destroy the goutweed before it spreads any further. This is an instance where even smothering the area with cardboard topped by a thick layer of mulch may or may not succeed over time because the plant has amazing reserves as you have discovered; instead I would recommend applying glyphosate when the plants are in active growth according to the label instructions. Once you are certain the goutweed is completely gone go ahead and replant.
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