The troubles with the HD-DVR's "check switch" I described a few days ago gradually disappeared over the course of a few days. I'm always suspicious of things like that; when will it come back without warning? What caused it? So I didn't cancel the appointment to have someone come out to repair it today.
I was unable to get it to repeat with any certainty, but while they were here, they realigned the satellite dishes to slightly improve signal strength. They showed no interest in the shiny silver box that I wondered about, and nothing they did identified or altered the source of the original problem. All we can do is hope it stays away.