Anyway, we bought a new counter-depth fridge, which is a great concept because it doesn't stick way out into the kitchen, and the shelves aren't so deep that things get lost back there. Even the plug is low profile, allowing it to snug up to the wall. At least it would snug up if our water valve wasn't sticking straight out of the wall.
I had to do something about this. My plan was to remove the elbow that was thrusting it outward and install a receptacle.
I started by opening things up to see what was going on in the wall.
Then came the blowtorch. It was frustrating because this valve is apparently the lowest point in our home's plumbing, so it dribbled water for a very long time before I could work on it. Eventually I was able to remove the offending elbow.
All connections made.
And here's the finished product.