I know that I am a week late, but I found a one-line change to your original code that think is worth sharing. Use the function substr rather than s/// to insert the id. Note that you already have $+{text} from your first match.

use strict;
use warnings;
use Test::More tests=>3;
my @required = (
    qq(<h2 id="match_literal_text">)
        .qq(2.1. Match Literal Text</h2>\n),
    qq(<h2 id="match_nonprintable_characters">)
        .qq(2.2. Match Nonprintable Characters</h2>\n),
    qq(<h2 id="match_one_of_many_characters">)
        .qq(2.3. Match One of Many Characters</h2>\n),
);

my @ol_file_array = (
    "<h2>2.1. Match Literal Text</h2>\n",
    "<h2>2.2. Match Nonprintable Characters</h2>\n",
    "<h2>2.3. Match One of Many Characters</h2>\n",
);

my $regex = qr/
    (?<tag>(<\w\d))
    (?<closing_bracket>>)
    (?<ol_numbers>(\d\.(\d+?)\.))\s
    (?<text>(.+))
    (?<closing_tag>(\b<\/\w\d>))
    /xms;

foreach (@ol_file_array) {
    if ($_ =~ m/$regex/g) {
        substr($_, 3, 0) = changer( $+{text} ); 
        ok( $_ eq shift(@required), $_ );
    }

    else {
        ... # blah blah blah
    }

}

sub changer{
    (my $id = $_[0]) =~ tr /A-Z /a-z_/;
    return qq/ id="$id"/;
}
[download]

OUTPUT:

C:\Users\Bill\forums\monks> tony3.pl
1..3
ok 1 - <h2 id="match_literal_text">2.1. Match Literal Text</h2>
#
ok 2 - <h2 id="match_nonprintable_characters">2.2. Match Nonprintable 
+Characters</h2>
#
ok 3 - <h2 id="match_one_of_many_characters">2.3. Match One of Many Ch
+aracters</h2>
#
[download]