You can easily remember 4 to 6 random words. You really will be surprised how quickly it is to memorize and type after a day or two. Mixing them up with what separator (if any) that you use, and if you number/special character substitute that adds dozens of possible permutations on a single password. And just using 4-letter words (over 100,000 in the English language) leads to a 100 quintillion possible passwords without any separator or character substitutions.
The next requirement should be no arbitrary changes to passwords. End users should be able to pick a strong 16 character password (based on uniqueness and the other password strength tools they recommend in the article) and only change it if they forgot it or a breach of their account is suspected.