UPDATED

foreach my $alphabeta (
  my $z;
  grep { $z = $_; grep { $z eq $_ } @alphas } @betas ){
  # do something
}
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Granted this still has the same problem as the initial code, but it's twice as fast and saves memory over your speedier (20xOriginal) solution. It also has the side-effect of effectively uniq-ing @betas. If you don't like that replace the outter grep with map.

--
perl -pew "s/\b;([mnst])/'$1/g"