I would like to wrap each section in an HTML <section>. Also, the subroutines (line, heading, and paragraph) used in story print immediately. It appears to get the table of contents, I will have to go through the lines twice.

sub story {
  my ($source,$author) = @_;
  my $tab = 3;
  
  my @toc;
  while (my $line = <$source>) {
    chomp($line);
    if ($line =~ /^2/) {
      my ($number,$text) = split(/ /,$line,2);
      push @toc, anchor($text, { href => '#'.idify($text) });
    }
  }
  
  list($tab, 'u', \@toc, { class => 'two' });
  
  # I ran $source above, so I can't have it here! /me head desks.
  while (my $line = <$source>) {
    chomp($line);

    # If a line starts with a bracket, just print the line.
    if ($line =~ m/^</) {
      line($tab,$line);
    }

    # If a line starts with a numeral 1-6, print a heading.
    elsif ($line =~ /^[1-6]\s/) {
      my ($heading,$text) = split(/ /,$line,2);
      my $id = idify($text);
      heading($tab,$heading,$text, { id => $id });
    }

    # If a line is a break or horizontal rule, print the line in brack
+ets.
    elsif ($line =~ /^[bh]r$/) {
      line($tab,"<$line>");
    }

    # All other lines are paragraphs.
    else {
      paragraph($tab,$line);
    }
  }

  # If I wrote a story, I want people to know I wrote it at the bottom
+.
  paragraph($tab,"written by $root_user", { class => 'author' }) if !$
+author;
}
[download]

How about delayed execution? You push all commands onto a stack and only execute after reading all data:

sub story {
    my ($source,$author) = @_;
    my $tab = 3;
    
    my @toc;
    my @commands;
    push @commands, [ \&startsection, "Lead" ];
    
    # I ran $source above, so I can't have it here! /me head desks.
    while (my $line = <$source>) {
        chomp($line);
        
        # If a line starts with a bracket, just print the line.
        if ($line =~ m/^</) {
            push @commands, [ \&line, $tab, $line ];
        }
        
        # If a line starts with a numeral 1-6, print a heading.
        elsif ($line =~ /^[1-6]\s/) {
            my ($heading,$text) = split(/ /,$line,2);
            if( $heading == 2 ) {
                push @toc, anchor($text, { href => '#'.idify($text) } 
+);
                if( $commands[-1]->[0] eq \&startsection ) { # not sur
+e this comparison is valid...
                    pop @commands; # to avoid empty sections
                } else {
                    push @commands, [ \&endsection ];
                }
                push @commands, [ \&startsection, $text ]; # adapt arg
+uments as required
            }
            my $id = idify($text);
            push @commands, [ \&heading, $tab,$heading,$text, { id => 
+$id } ];
        }
        
        # If a line is a break or horizontal rule, print the line in b
+rackets.
        elsif ($line =~ /^[bh]r$/) {
            push @commands, [ \&line, $tab, "<$line>" ];
        }
        
        # All other lines are paragraphs.
        else {
            push @commands, [ \&paragraph, $tab, $line  ];
        }
    }
    push @commands, [ \&endsection ];    

    # do the table of contents
    list($tab, 'u', \@toc, { class => 'two' });

    # delayed execution of all print commands
    for (@commands) {
        my $cmd = shift @$_;
        $cmd->(@$_);
    }

    # If I wrote a story, I want people to know I wrote it at the bott
+om.
    paragraph($tab,"written by $root_user", { class => 'author' }) if 
+!$author;
}
[download]

I cannot test this code but it hopefully conveys the idea...

startsection and endsection would be two subs to print the HTML to start and end a section.

Update: some changes in formatting of the post and added a missing comma in the code.

Update: added a missing endsection at the end.

I think I got it, however, I didn't use your code. I'm sorry. Here is how I did it.

sub story {
  my ($source,$author) = @_;
  my $tab = 3;
  
  my $inc = 0;
  my @sections;
  my @toc;
  while (my $line = <$source>) {
    chomp($line);
    
    if ($line =~ /^2/) {
      $inc++;
      my ($number,$text) = split(/ /,$line,2);
      push @toc, anchor($text, { href => '#'.idify($text) });
    }
    
    push @{$sections[$inc]}, $line;
  }
  
  list($tab, 'u', \@toc, { class => 'two' }) if @toc > 3;
  
  for my $section (@sections) {
    section($tab, sub {
      for my $line (@{$section}) {
        chomp($line);
        if ($line =~ m/^</) {
          line($tab,$line);
        }
        elsif ($line =~ /^[1-6]\s/) {
          my ($heading,$text) = split(/ /,$line,2);
          my $id = idify($text);
          heading($tab,$heading,$text, { id => $id });
        }
        elsif ($line =~ /^[bh]r$/) {
          line($tab,"<$line>");
        }
        else {
          paragraph($tab,$line);
        }
      }
    });
  }
  
  paragraph($tab,"written by $root_user", { class => 'author' }) if !$
+author;
}
[download]

No matter how hysterical I get, my problems are not time sensitive. So, relax, have a cookie, and a very nice day!
Lady Aleena