Thanks for the thoughts. My shocks are a few months old, but there could be a bum.
After more testing, it only happens after I turn the wheels all the way to the right. I don't notice it after I turn the wheels to the left.
I did notice that the steering damper has a dead spot when you start to compress it from being fully extended. I don't know if it gets fully extended while in place. I imagine there's some margin to prevent pulling the damper apart. If a fully extended damper corresponds to the wheels turned to the right, that could be it.
And that's a reminder to check that my steering box is securely mounted to the frame.