Move project info to new template

I have an existing project file that I would like to move the contents of to a new template that I have made visual changes to.

When I open my project file, I select all tasks in outline view, copy the information (CTRL + C), open my new empty template file, then paste all task info into the new template file. The issue is that all task information for start and end dates is replaced using the template start date.

Is there a recommended way to “Copy exactly” so I don’t have to adjust dates manually?