Hi – I’ve had a lot of couch to deal with over the years and have found that – like many problem weeds like sorrel too – successive years of mulching does as much as hand weeding – it simply seems to make the ground less hospitable and they vanish in about 2-3 seasons. On non veg borders I typically alternate bark, municipal compost and mushroom compost in a pretty hefty layer applied in April.
Best of luck !
