I was unaware of Acme::September::Eternal until today. A couple of years ago in my ignorance I wrote a little script to perform essentially the same task, albeit just for the current date.
Looking into the source we can see that Acme::September::Eternal makes use of Date::Manip (as you mention) and Lingua::EN::Numbers::Ordinate whereas my solution is based on Time::Piece and Lingua::EN::Inflexion. Mechanical details aside, they are practically the same. TIMTOWTDI indeed.
Here is a redacted version of mine, for anyone interested.
use Lingua::EN::Inflexion 'inflect';
my $now = localtime;
my $then = Time::Piece->strptime ('1993-08-31', '%Y-%m-%d');
my $diff = $now - $then;
$diff = int ($diff / 86400);
my $day = inflect ("<#o:$diff>");
print "Today is the $day of September 1993\n";