I'm not sure if you have multiple data sources, or if you are using a single data source with multiple connections - but if you are using just a single data source, you can extract the data into a .tde file quite simply. Navigate to a sheet view, then hit Data -> (name of your data source) -> Extract Data...
You should then be able to create a new tableau file by connecting to the .tde source, and begin working.
Let me know if this helps!
Thank you for your quick response! Unfortunately, this didn't quite work. I have a variety of charts and calculated fields set up that I don't want to recreate. I ended up using this link: Changing the File Path for Extracts | Tableau Software to create different extracts for each file. I'm still having some minor issues with extracts defaulting to the TEMP folder, but this worked out with minimum recreation.