It's actually normal to fire the first spot in a break as you're saying the last syllable in your break.
You're right, the cut-off is totally predictable. So the solution is to compensate with a delay.
Listen to WABC's stream and you'll hear over and over, "This is BlaBlaBla for WAB-."
Add an automatic half-second delay to the cut-off for God's sake! Or delay the mute. Technology is wonderful as long as people care enough to use it correctly.