My last comment, don’t be afraid of chemicals irrationally. Don’t be afraid of all the lawsuits that are obviously glorified ambulance chasers latching onto the next big thing. Do have a healthy fear of chemicals. Have respect for them, and wear proper PPE. They are tools that can be used in certain circumstances. I recommended the herbicide route because that’s the quickest and easiest route to solve your problem and start over. It’s not a long term solution, nor is it the be all end all of your lawn care. And, as I said, check your local extension office. I guarantee they have a page dedicated to controlling that weed, along with prescribed treatments. Those are the true pros who study these things and can set you straight.