Regardless of your interest in spoken Latin, taking an old reading from a previous class and summarizing it is a powerful tool. The time it takes to retell a story in simple Latin is marginal, your students get repetition of vocabulary and grammar in context, you can use words and structures from their later lessons in a familiar context to build comprehension... what's not to love?
If you're not confident speaking Latin off the cuff, practice retelling the story in the car or shower. Write it down in your own words and read it, if you have to. When you read the advice of the Latin teachers of old, almost without exception they recommend this. They were onto something, and let's be honest, here. Most of them weren't running around talking Latin in the street. If they can do it, you can too.
Teaching the pretty little grammar is great. Circle the classroom with your CI thing of choice, if that's your style. But whatever you do, retell the stories. Your students will thank you.