Given the necessary modification to exists_ggg:

sub exists_ggg (\%;$) {
    my($h,$k) = @_;
    my $c;
    grep { length == length $k } grep { /\Q$k\E/ } grep { ++$c % 2 } %
+$h;
}
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Just in case anyone had any doubts regarding the efficency of exists alternatives:

               Rate exists_ggg exists_srk     exists
exists_ggg   5394/s         --       -68%       -98%
exists_srk  16784/s       211%         --       -92%
exists     219707/s      3973%      1209%         --
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If you're really worried about that 219707-th of a second, you've got bigger problems...