Moving forward, make project folders for each project and set the file path preferences for the subfolders. But you probably knew that.
You could use the move or copy features and duplicate new project folders with the Reaper file dialog window features. Probably much quicker and straight to the point to just do it in a Finder window and be done with it though. (Explorer window in Windows) Use the features to sort by filename/type/date etc and knock it out. It IS literally what the feature set there is made for. File handling.