They should probably broadcast a few days past the cut-off. But only broadcast a static screen that says "Analog TV transmission has now ended.
Or broadcast only the first twenty minutes of a few half-hour shows. Maybe the first twenty minutes of an episode of "Greenacres," followed by twenty minutes each of "Rhoda," and "The Mouseketeers." Rotate through those three same segments every hour, and see how long it takes for people to figure it out.