How should I migrate my iTunes library to a larger external disk while preserving metadata?
So I successfully migrated the library without losing the metadata by:

1) Changing the default library under iTunes > Preferences > Advanced > to /Volumes/MEDIA_4TB first 

2) Selecting all the contents of the library within iTunes. 

3) Going to File > Library > Consolidate Files

After many hours of copying, I confirmed it worked by right clicking on a movie > Movie Info > File Tab > Location: /Volumes/MEDIA_4TB/Movies/[Name of Movie]. I can now safely delete the contents of the old 2TB drive and reformat it.