Somewhat unrelated to your question, but this if needs an else. You use $year later, and don't otherwise reset it:

if ($file_in_question =~ /^(\d{4})/){
  $year = $1;
}
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As for your actual question, does this work?

print OUT for map{
  s[(^\d+\s+)[\d\.]+\s+][$1];
  "$year\t$_";
} sort { 
# ... etc.
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addendum: I would follow BrowserUk's advice in Re^3: Regex problem and replace the map pipeline with a series of steps. You aren't comfortable with this code the way it is.