The solution I discovered is this...

$contents =~ s/(<IMG\s.*?>)/&addalt($1)/sige;
$contents =~ s!\>alt=\"\"! alt=\"\"\>!sig;
print $contents;

sub addalt {
   my $returned=shift;
   if ($returned!~m/\salt/){
      $returned=$returned.'alt=""';
   }
   return $returned;
}
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The key I discovered was the "e" switch on the regex.