The easy solution to your regex problem (although Text::Balanced is probably an easier solution to your general problem) is to just maintain modularity:

use strict;
use warnings;
no warnings qw /uninitialized/;

# \A anchor removed, so this is the same regex from the perlfaq.
my $re;
   $re = qr{
             \(
             (?:
                (?> [^()]+ )    # Non-parens without backtracking
              |
                (??{ $re })     # Group with matching parens
             )*
             \)
          }x;

while (<DATA>) {
    chomp;
    print "$_: ";

    # here is the proper place for the anchor
    print $& if /\A$re/;
    print "\n";
}

__DATA__
(*********)
(***(*)***)
((***))
(((***)))
((**)**(**))
(((())))
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