Anne Get an old meat cleaver -- if you lived nearby I have one you could have -- and use it to make your slot. You could certainly hammer it down to break the roots apart. It would take some time if you have a hundred feet to go, but it would do the trick even if it was slow going. I suppose a square shovel would let you do the same thing, probably much quicker! Then, as you note, you could use a cheaper material for the root barrier. I've no idea how long grass roots are; it must depend on the type. But you could water a small area until it's soggy and gently pull up on some of what's there to get an idea of the root length. With a barrier AND a 10-12 inch extension, you aren't likely to get much invasion from the other side!

I would like to mention that this is a great thread; if I had read something like this when I began planting herbs it would have saved me a lot of trouble! I am in Pennsylvania, USA, zone 6, with rich clay soil and good rainfall. Our summers can be quite humid, and my property has several mature trees, so never gets truly full sun. When I started a little herb garden years ago I had no idea of the growth habits of any of the herbs, as I had never seen any of them growing in a garden (or anywhere else, for that matter). The references I was able to access at the time were little help. I returned to work shortly after that, and the next time I was able to give attention to my herb garden, the lemon balm/mint had completely overgrown all of the other herbs! It eventually seeded itself in little clumps all over my yard. I sometimes wish I hadn't pulled quite so much of it up, as it eventually subsided and practically disappeared. I found myself planting more of it last fall, as I am drinking more herbal teas these days, and also to compete with Yellow Archangel (an even bigger mistake I made more recently). I had the same experience with the purple-flowered agastache--"Korean Hysop," it easily gets two feet tall in medium shade and spreads by seeding itself all over the place--but it is easily pulled out and makes a good addition to herbal teas as well. Bee balm, on the other hand, will grow for me, but has never been particularly invasive; on the contrary, it seems to die out after a few years. Since I really don't get full sun, which catnip prefers, it has never done well enough for me for it to become a problem. Thyme and sage will overwinter for me, but only in pots. Thyme is so tiny it is easily overwhelmed by almost anything else, and I never plant it directly in the ground anymore, as I always lose it. I have found it will fill a gallon pot or equivalent container if kept to itself, however. Oregano will overwinter for me, but it has never become invasive; it is so low compared to many other herbs that it needs to be kept next to the edge of a bed, or in a pot. Coltsfoot will really take off and quickly cover a large, cultivated area--it is viny--but it died out after a few years, and I really don't consider it a problem under my conditions because of that (except in a small bed with other things that you want to survive, of course.) Lovage can get to four or five feet tall, with numerous leafy stalks. Even it can be shaded out by Angelica Archangelica, which develops wider leaves and can cast more shade. The Angelica A. I have in my garden right now was started last summer, and is about 3 1/2 feet tall, with leaves that extend out like wings for about 18 inches each. The central stem is about 2 inches thick. Comfrey will shade out anything in a four to six foot radius. Its leaves and stalks will initially grow straight up, but then collapse into a circle around the plant, smothering anything underneath. My most recent experience with invasive herbs was with Motherwort. I bought one small plant at Sturbridge Village a few years ago, and it spread through the back fourth of my yard by seed, even in lawn! It makes copious seed, as it gets about two feet tall, has numerous tiny flowers at every leaf node along the stem, and is a sturdy plant that gets spiny as it matures. It is not that difficult to pull out with gloves, though, and the young plantlets appear to be controllable by mowing. Ref. the comment above about tomatoes--even in my climate zone, a popular little yellow salad tomato has occasionally come back the next year in my husband's vegetable garden.

The cardboard will very effectively keep sunlight from reaching any plants that attempt to grow under it therefore keeping them from growing. There is no reason to put down a pre emergent weed preventer as well, a product that only keeps seeds from rooting. If you have an invasive unwanted plant, such as Bindweed, the pre emergent will not be effective anyway and the cardboard may do more to control that.

Yes, winter grass will take over by shading out the desired grass until it dies back in summer, but since it is an annual you can control it by not letting it go to seed by pulling it, or prevent the seed from sprouting by using pre-emergence weed killer applied at the right times which is usually twice in the fall. You can look up when the right time is right for your area. I have not found that corn gluten helps much, but the commercial products do very well in stopping the sprouting. I had a lot of it and though it's a lot of work to pull it, but that's what I did. I used a digging fork to loosen the whole area before pulling and also applied the pre-emergent the next fall. Now I have very little problem, just have a few sprouts that I pull as soon as I see them. With all the rains this year I've had more come up than usual. My neighbors don't control their so the seeds blow in. Keeping it mowed short helps a little, but it learns fast to grow low and send the seed heads out horizontally. I tried using Grass-B-Gone being very careful to spray only the center of the grass, but apparently it leaks out through the roots because it killed the good grass for about a foot around it. I do use Grass-B-Gone in flower beds for Bermuda grass mostly since it only kills grass. So yes you can get rid of it, but it takes a little time and work at the first. Wishing you well!