Algorithm::Loops' NestedLoops allows a non-recursive implementation:

use Algorithm::Loops 'NestedLoops';

sub find_path {
  my ($adj_list, $length) = @_;
  my %been_there;
  NestedLoops([
     [sort {$a <=> $b} keys %$adj_list],
     (sub {
        # The last value on @_ has just changed, so remove it from %be
+en_there
        # and set the new one
        my ($last_position, $last_value) = ($#_, $_[-1]);
        delete $been_there{$_} for grep $been_there{$_} >= $last_posit
+ion, keys %been_there;
        $been_there{$last_value} = $last_position;
        # Here I grep out the already-visited nodes, but you could als
+o exclude
        # any letters that don't result in prefixes of real words.
        [ grep !defined($been_there{$_}), @{$adj_list->{$last_value}} 
+]
      }) x ($length-1)]
  );
}

my $i = find_path(\%adjacency_list, 3);
my @path;
print "@path\n" while @path = $i->();
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