Sorry for the delay.

I do read in the whole file at once and pass it as a variable to XML::Twig and make three consecutive passes. Here are the first, second, and final passes. The first pass just collects some information, the second pass actually starts processing the elements. The are a few map and grep functions used in the various handlers (not listed):

...
my $xml = XML::Twig->new(
    pretty_print => 'nsgmls',   # nsgmls for parsability
    output_encoding => 'UTF-8',
    twig_roots => {  'office:automatic-styles' => 1 },
    twig_handlers =>
    {
        'style:style[@style:family="text"]/style:text-properties' => \
+&handler_style_collector,
            'style:style' => \&handler_paragraph_style_collector,
    }, );

# $content is not saved from the first pass, it only builds some hashe
+s
$xml->parse($content);
$xml->dispose;

$xml = XML::Twig->new(
    pretty_print => 'nsgmls',   # nsgmls for parsability
    output_encoding => 'UTF-8',
    twig_roots => { 'office:body' => 1 },
    twig_handlers =>
    {
        # link anchors (text:boomark) must be handled before
        # processing the internal links (text:a)
        '*[text:bookmark]' => \&handler_bookmark,
            'text:note[@text:note-class="footnote"]/text:note-body'
            => \&handler_footnotes,
            'text:note-citation' => \&handler_citation, # only some ki
+nds
            'text:span' => \&handler_span,      # typographic markup
            'text:list-item' => \&handler_list_item, # all lists becom
+e unordered
            'table:table-header-rows' => \&handler_table_header_rows,
            'table:table-row' => \&handler_table_row,
            'table:table' => \&handler_table,   # primitive table supp
+ort
            'text:line-break' => \&handler_line_break,
            'text:table-of-content' => sub { $_->delete },
            'text:index-body' => sub { $_->delete },
            'text:alphabetical-index' => sub { $_->delete },
    }, );

$xml->parse($content);
$content = $xml->sprint;
$xml->dispose;

$xml = XML::Twig->new(
    pretty_print => 'nsgmls',
    empty_tags => 'html',
    output_encoding => 'UTF-8',
    twig_roots => { 'office:body' => 1 },
    twig_handlers =>
    {
        # links (text:a) must be handled after the link targets (text:
+bookmark)
        'text:a' => \&handler_links,

            'text:h' => \&handler_h,
            'text:p' => \&handler_p,
            'draw:frame' => \&handler_draw_frame,
            'office:annotation' => sub { $_->delete },
            'office:annotation-end' => sub { $_->delete },
            'text:sequence-decls' => sub { $_->delete },
            'text:tracked-changes' => sub { $_->delete },
            'text:table-of-content' => sub { $_->delete },
            'office:forms' => sub { $_->delete },
            'text:list' => \&handler_lift_up,
            'text:section' => \&handler_lift_up,
            'office:body' => \&handler_lift_up,
            'office:text' => \&handler_lift_up,
    }, );

$xml->parse($content);
$content = $xml->sprint;
$xml->dispose;

. . .
[download]

The first pass is necessary to collect some information about typographical markup before actual processing begins. Then there are some manipulations which have to be kept separate for the second and third passes, but that helps because spreading some of the other handlers across the two passes seems to speed up processing.

Then there is some regex tidying of the markdown stored in $content afterward. It seemed best to do that as regex.

It's a bit moot at this point, though: While the script does the job quite nicely on the use-cases I've tried it on, the person I wrote it for has access to additional data (for his specific use-case) so he was inspired to write a second version which is more tightly couple with that data.