You know, I am wondering if 'my' weed is Creeping Charlie. The online info refers to blue flowers in the early spring: the weed with which I am obsessed does not have flowers unless it is left to grow stems. (At least I think that's what happens.) The photos online show leaves that are more deeply scalloped. Of course I could have another variety, and clearly whatever it is it is similar to other creeping ground covers. Anyway I have selected a few areas that are relatively large and manageable to conduct some experiments as suggested: hoeing out and monitoring, covering with cardboard and monitoring. I'll let you all know how it goes after a while. I have appreciated all the information and advice from this thread.