Hmmm ... I am not very comfortable with interpreting $_. I don't know how to print $masks{$_} to understand what it is. That is my problem. I know I am dumb!

    print $name."\n";
    print $letters."\n";
    print $masks{$_}."\n";
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which gives obvious error:
A
W       W       M       W       W       W       M
Use of uninitialized value $_ in hash element at ./parse-counts.pl lin
+e 37, <INPUTR> line 2.
Use of uninitialized value within %masks in concatenation (.) or strin
+g at ./parse-counts.pl line 37, <INPUTR> line 2.
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Replace

    $counts{$name}{$_} += ($masks{$_} | $letters) =~ /M/ for @unique;
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with

    for my $label (@unique)
      {
      print "$masks{$label}   |   $letters\n";
      $counts{$name}{$label} += ($masks{$label} | $letters) =~ /M/;
      }
[download]

This will allow you to see what you are or'ing