When multiple script controls are used to play different cues, one control cancels out the other. For example, I have a Script Control scheduled to start my announcements at 9:30. My service starts at 9:45, so I insert another Script Control to play a 5 minute countdown video at at 9:40. The Second Script Control gets me out of the looping announcements.
The same thing is happening with your current configuration, but since nothing is displayed with audio MediaShout will need to display something. And since you are playing timed cues, that timing is still used one last time. This causes the next cue to be played. Given the Script controls are actually working as designed, there isn't a way to change it without causing any additional issues.
However, a simple change in the way the Script is created should give you the results that you need. Please try this layout and let me know if it works for you.
Cue #1. Script Control targeting the Audio playlist 7:20 before service begins.
Cue #2. First Announcement Cue
Cue #?. Placed under the last Announcement Cue targeting Cue #2.
When the Script Control targeting the Audio playlist fires, it will play Cue #2, basically restarting the Announcements.
Hope this makes sense.