Geoprocessing tool "Apply label classes from layer"

[IlkaIllers1]

One of my workflows involves creating dynamic annotations that rotate with the rotation angle of each page of the map series. Since the pages often overlap, but have different rotations, at the beginning of the workflow I use a spatial join one-to-many where the join values is the polygon feature class containing the pages for the map series. This is followed by copying all label classes from the old feature class to the new spatially joined one. 

I would like to automate this workflow, but since right in the middle of it I need to manually copy and paste the label classes, it doesn't work as a model. 

I would be awesome to have a tool similar to "Apply symbology from layer" that grabs all label classes from another layer and simply copies and pastes them into the new one.