There was another run-time error. But for closure, the program is executing and I am listing the end result below.

The key was realizing the the anon array was really a reference to an anon array, which clicked in the dereference mode of thought ...

  if (!defined $WA{$key}) {
    {
      lock $WAlock;
      $WA{$key} = &share({}); #hook shared anon hash;

      {
        lock %{$WA{$key}};
        $WA{$key}{PS}=$dtg;          # PS period Start
        $WA{$key}{PE}=$dtg + $secs;  # PE period End
        $WA{$key}{PT}=0;             # PT period Total
        $WA{$key}{stags} = &share([]);
        for my $i (0..$rnds-1){
          ${$WA{$key}{stags}}[$i]=0;    # init all stages to 0
        }
      }
    }
  } # end of (! defined) entry being initialized

.... and .....
sub reportWA{  # $key
  my $key = shift;

  my $NewWA;

  unshift @{$WA{$key}{stags}},    $WA{$key}{PT};
  $NewWA=$WA{$key}{PT};    # $periodTotal * 1

  $#{$WA{$key}{stags}} = $rnds-1;
  for my $i (1..$rnds-1){
    ${WA{$key}{stags}}[$i] *=  $wght;  #stg[n] = initial * (wght**n)
    $NewWA += ${WA{$key}{stags}}[$i];
  }
  #plog sprintf "stages =  %s" ,join (", ",@stgs);
  $NewWA /= $rnds;
  printf " %d  %d  %8.2f    %s\n" , $key,$WA{$key}{PE} ,$NewWA,
                                 join (", ",@{$WA{$key}{stags}});
}
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Thank you all, and the speed was amazing..