Back with some pictures:
couch grass above
couch grass rhizome above
yellow nutsedge above
more yellow nutsedge above Other pictures I've found online seem to imply this weed likes wet soil. This is probably why it hasn't taken over my property because we are very dry and well-draining. Three years ago we had a little kitchen garden and an adjoining path that went around the house from the back door to the side/front deck. The path forked off, across the yard and down to our lower garage (which is now falling down). Long story short, the garden and paths became inundated with couch grass. You can pull forever, but those rhizomes stay and grow back. I forked up as many rhizomes as I could (discarded bushels of them). Placed new landscape cloth, mulched with small stone. I discarded the mulch and cloth from the path to the garage, filled in with soil and planted grass. On the stone path to the deck, I built a boardwalk. This is working fairly well, as I've only had to pull a few couch grass plants per year that poke through, or creep in from the rest of the lawn. I'm hoping this lasts for awhile.
Former kitchen garden above
Path and boardwalk to the deck above
Re-seeded old path above. The couch grass lives in the lawn and yes, it does grow higher and faster, but we can't really tell much difference because there's just so much of it all over. We are very rural and we get every weed seed flying through. Just doesn't make sense for us to try to get rid of them. I just try not to let them go to seed and to keep a sharply cut edge on my gardens (easier said than done).