I think that's the challenge ITA wants you to solve - recursing 300 levels deep into a list of 1000 movies will literally take forever. As you can see with the 2nd linked article, brute-force just doesn't work.
My original algo for the multi-word anagrams was nearly identical to what you described. The problem was when you entered a long phrase. You can form 8000 unique words from the letters in "William Jefferson Clinton." Even when I removed duplicates words with the same characters (art = tar = rat), it was still 7000+ long. Add in another 'r' or 's' to the original phrase and you're over 10,000 unique words. If I'm allowing my algorithm to make 5 word anagrams, that's 10^5 calculations for a single web query - absolutely impossible.
And even if I do magically return the 100k possible results in 0.1s, users can't parse through 100k results to find the ONE anagram that's funny or creative. I do have an idea of what I want to do. Maybe in a week or so, I'll have a demo working.