Looks great, but you didn't use any of the solution-space reducing tricks I suggested in the other thread. Oh well, it turns out that when you get close to the solution, in most cases all the numbers get into the candidate lists.
In the inner loop, I think assigning to a hash is cheaper than deleting from it, so it might be better to assign 0 or undef instead of removing elements.
You mentioned not seeing an algorithm for permutations of n distinct numbers taken r at a time. You could use Algorithm::ChooseSubsets to select the elements, and then permute them with Algorithm::FastPermute.