The hose itself has been in need of a new connector for some time, so this is actually a twofer.
The first part was easy. I cut a couple inches off the end and installed the new connector. I even sprung for the fancy metal one.
The next part was much more challenging. Try as I might, I couldn't unscrew the old hose connector from the malfunctioning valve or the rest of the wand from the valve. They all seem to have become welded together over time. I soaked everything in vinegar, hoping it would dissolve the minerals holding everything together.
I tried to get the old connector out of the valve until the connector ripped apart, then I tried getting the wand off the valve, which worked. So I managed to salvage the wand, but now it doesn't have a shutoff valve. Good enough.