while ( @files ) {
    my $num_to_submit = ( @files > 6 ? 6 : @files );
    my $f1 = shift @files;
    my $f2 = shift @files;
    my $f3 = shift @files;
    my $f4 = shift @files;
    my $f5 = shift @files;
    my $f6 = shift @files;
      ...
    $mech->submit_form(
        ...
        fname1 => $f1 || '',
        fname2 => $f2 || '',
        ...
        fname6 => $f6 || '',
    );
  }