Can't you just use two separate scopes?

{
  {
    my $mech = Test::WWW::Mechanize::Catalyst->new(
      catalyst_app => "CoolCatalystApp" );
    run_tests( $mech );
  }

  change_config();

  {
    my $mech = Test::WWW::Mechanize::Catalyst->new(
      catalyst_app => "CoolCatalystApp" );
    run_tests( $mech );
  }
}
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