Not sure if I understand your requirements fully, but this works for me:

for my $p ($xhtml->findnodes('//blockquote/p')) {

    my $text = $p->as_text();
    $text =~ s/^\s+//;
    $text =~ s/\s+$//;

    if ( $text =~/\n\s*\n\s*/ ) {
        my @paragraphs = split(/\s*\n\s*/, $text);
        my @new_elems;
        for my $para (@paragraphs) {
            my $new = HTML::Element->new('p');
            $new->push_content($para);
            push(@new_elems, $new);
        }
        $p->replace_with(@new_elems);
    }
}
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