I've been fighting this too for 4 years now. Actually I've had it for a long time and the patch was was just getting bigger and bigger. I should have sprayed it 12 years ago when I first spotted it. Control in the past consisted of roundup and then reseeding. However I would have mixed results. I would get patches of it growing here and there. I'm about 60 percent done now, but like some of you the seed keeps coming back. This year I've tried something else. I've dug up some sprayed stuff and laid sod but man that's just too much work so I took a weed burner and have burned anything yellow. I'll keep some fertilizer on the burned spots and keep spraying and burning it till fall then using a small rototiller, till my soil and mix a bunch of seen and starter bed stuff together and replant the bare spots again. Hoping this is the last of it.

I have had some success spot spraying triclopyr + fenoxaprop tank mixed to control creeping bentgrass in my KBG lawn. It will probably take 2-3 applications but it does a number on creeping bent and nimblewill. Mesotrione will be great for creeping bentgrass but it is not approved for residential lawns as yet so even a professional cannot apply it for you.

If you have a solid area you want to clear, smothering would be the easiest, least toxic, and very effective against something as 'soft' as Glechoma. You can get large pieces of cardboard from furniture/appliance store, much easier to handle and stronger than newspaper. Mow everything as low as possible, then cover completely with cardboard, overlapping generously. Getting it wet, then walking all over it will help it conform to the ground. A cover of mulch or mulchy-looking leaves will keep it from blowing away, and give it enough weight to smash the weeds and prevent them from being able to keep growing. Also fixes the appearance instantly, looks like a yet-unplanted mulched bed, which it is. The cardboard will decompose and does not need to be removed. Wait at least a month before piercing to add any new plants.

I'm a little hard on people who come here claiming to have been reading THIS forum and then presenting a plan that flies in the face of what we talk about. Had you been reading THIS forum you would not have already killed your grass. As j4 has mentioned, this is a poor time to be renovating a lawn. Today is better than tomorrow and that will continue until September, but really (REALLY) early fall is by far and away the best time to renovate northern grasses. Simply keeping the weeds mowed goes a long way toward a nice looking, and playable lawn. I've been mowing weeds for going on 3 years as my St Augustine creeps back from nothing. Weeds are green. Don't rototill. I did some historical research to see who first advocated rototilling. I wanted someone to blame. The old gardening books from the 40s through 70s advise against tilling for a lawn. More recently you do see articles advocating it. Even the Scott's website says to start with rototilling. In their case I have to question their motives, because you are likely to buy more products (from them) if you start by rototilling. I never did find the root of the problem, but rototilling will give you a bumpy surface from Day 1 and continue until about Day 1,000. After about 3 years the soil has settled, developed a firm structure, and should not get any bumpier. Mowing a bumpy lawn is not fun. Don't bring in new soil unless you are sure your drainage is poor or you have low spots that hold water for more than a day after a long rain event. New soil will ALWAYS change your drainage. What you don't want is water getting dammed up by the lawn and backflowing into the house or basement. Maybe it's an optical illusion but it looks like the soil goes up from the walkway. It looks like it goes up through the plants, up past the bricks, and finally crowns in the center of the yard. It should start to fall away immediately from the walkway and slope gently down to the front sidewalk. If I'm seeing that correctly you need to have about 3 cubic yards of soil hauled away (as a start). Your idea to bring in new soil is very common. Again I'm not sure where that got started. It is also a commonly held belief that you need to topdress with sand or top soil every year. Golf courses do this but they are trying to counter attack a very specific fungus that does not occur for homeowners. Golf courses don't have basements either. If you think you need new soil because it will be a better product than you currently have, it is NOT. Your soil already has all the microbes it needs. New soil has some, but it has been disturbed which kills a bunch of them. Leave well enough alone. If you want to tune up your soil chemistry that can be done with a good soil test. If you want to improve your soil biology, then use organic fertilizers and avoid fungicide and insecticides.