I am glad you liked the article and welcome to the site.
Have a look under’No dig vegetables’ for pics of cardboard on top, which I find most effective as otherwise, when buried under compost, it rots more quickly and weed roots and shoots can then grow up through it.
OR you may find that 6 inches of compost/manure is enough, without cardboard on top, to weaken the couch to a point where its new growth is so weak that regular trowelling of regrowth in the first year after mulching can eliminate it.
What about paths and couch spreading in from them? Maybe mypex? or cardboard for them.