package MyThing;

use Exporter qw(export_to_level); # no need for inheritance here.
use Import::Into; # magic

our @EXPORT = qw( $BY_SIZE $BY_DATE $BY_USER );

sub import
{
  shift->export_to_level(1); # handle our exports
  Object1->import::into(scalar caller); # calls Object1's import method but uses magic.
}

#...

package Object1;

# has to handle its exports here as if it were in its own file.

1;