First of all, I understand your frustration. When we moved to our little acreage eleven years ago, I tried everything to pull it out but to no avail. We
still have it everywhere in our front yard, but now, I have actually embraced it. I know that doesn't
answer your question, but I truly find it a beautiful plant that I enjoy harvesting on a regular basis. I tried a few things to get rid of it, too, but something switched in me, and I actually started to see it as attractive. Sometimes it even flowers, and the flowers are gorgeous, like baby's breath. Have you ever
tried eating it? I put in as green with whatever I am cooking, and it adds a nice flavour. Mowing helps keep it under control, and you try overseeding your grass, too.
I will say, though, that now there is actually less of it than there was when we started. Us just "leaving it" has actually resulted in it less of it overall. I have no idea why that it is, but just reporting what has happened. We just mow what's there with the rest of the lawn, and although it's not a monoculture, it all flows together.