Avoiding direct eye-contact with your question momentarily, I point out that

package BigThing;
sub new {
      shift;
      bless $self, "BigThing";
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is very bad. It makes subclassing BigThing very difficult.
It even makes code re-use by cut-and-paste more painful than it needs to be.

The constructor is passed the class name; it may as well use it:

package BigThing;
sub new {
      my $class = shift;
      bless $self, $class;
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