Best way to convert existing documents into new native file templates

Hi, all! I have been working on marketing materials in InDesign for several years now. I recently found out that the materials are getting a redesign. I will be sent the new native file templates. I need to find the best way to "convert" my existing materials (all documents) into these new templates. 

I'm thinking the best way is through copying and pasting the elements of one of our old pages into the new template, and then tweaking as needed? I'm not sure if that's the most effective or efficient method, though - I need to update dozens and dozens of documents. 

Thanks in advance!