I haven't completely figured it out, but I have determined that you can add a head1 with code like this:

use Pod::POM;

my $parser =  Pod::POM->new();
my $pom = $parser->parse_file(...);
my $h1 = $pom->add($parser, 'head1', 'This is a new head1');
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and the new head1 will appear at the end of the POD. However, I don't think it will be easy to add a a head1 section in the middle of the document (in case you want your sections to follow a uniform ordering). In that case, something like this might work for you:

my @SECTIONS = qw(name synopsis ...);

my $pom = $parser->parse_file(...);
my %found;
for my $h1 ($pom->head1()) { $found{lc($h1->title)} = $h1; }
for my $title (@SECTIONS) {
  my $h1;
  if ($h1 = $found{$title}) {
    print $h1;
  } else {
    print "=head1 ", uc($title), "\n\n";
  }
}
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Of course, this code silently discards sections that are not listed in @SECTIONS which is probably not what you want to do, but it at least is a start.