Hi,
I inherited my plot from a charming gent who lovingly tended it for about forty years. Sadly, I also inherited his mares’ tail. Now, he did warn me not to let it get into the compost. However,after reading “ No Dig Organic Home & Garden” maybe I can add the hoed tops to the pile.
Phil, all mine have gone in to the compost pile over the last five years. It all disappears along with anything else that I can lay my hands on! Mulch the worst areas for a year or two with thick plastic and then be ruthless with your hoe and trowel from then on. It’s possible to almost eradicate 🙂 Good luck.