Reading TAR.GZ (full of texts/ XML / XBRL) - please provide fme_basename

TAR.GZ (full of texts/ XML / XBRL):

Using a CSV reader, no attributes are available to tell me which file each line was read from (e.g. fme_dataset, fme_basename, fme_featuretype, etc. are not coming out useful).

I have over 7k of these tar.gz files (nearly 1.5TB) and would prefer not to unzip them (blows up to ~9TB) just to be able to wildcard the reader appropriately / know which file each line is coming from.