I'm thinking that main subroutine could be more cleanly written as

sub find_common_parent_node
{
    my( $dir1, $dir2 ) = @_;

    my @dir1 = ( $dir1->volume, $dir1->dir_list );
    my @dir2 = ( $dir2->volume, $dir2->dir_list );

    my @sharan;

    while ( @dir1 and @dir2 and $dir1[0] eq $dir2[0] )
    {
        push @sharan, shift @dir1;
        shift @dir2;
    }

    # if needed:
    my $dir_A = dir( @dir1 );
    my $dir_B = dir( @dir2 );

    dir( @sharan )
}
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but I may be missing something (besides the debug code...)