Yeah, we’ll need to support E="b" (extended report) properly in blockmedian, since right now it’s hardcoded to use the columns from the input dataframe (see https://github.com/GenericMappingTools/pygmt/blob/60eb50592a564723f98c19bd452c2debcd6098f7/pygmt/src/blockm.py#L59-L61).
Could you open a general feature request at https://github.com/GenericMappingTools/pygmt/issues/new?assignees=&labels=feature+request&template=feature_request.md&title= for adding E="b" to blockmedian? Even better if you have time to implement it directly in PyGMT 