Is there a password hash function with a human component?
Answer: No.

Reason: Useless.

Explanation:


Not necessarily perfectly reproducible as crowds of people may give different output. So you will end up introducing some degree of tolerance.
Once introducing that degree of tolerance, pattern recognition algorithms will be able to automate that and possibly even achieve a higher accuracy than the humans.
NSA will hire many cheap labour agents and manage to get them work for you and cause your hashes to be insecure. NSA is rich, they can hire many of such cheap labour. How can you ensure that the many humans that are solving hashes for you are actually honest people that are not NSA agents?


My opinion: you are trying to solve an existing problem (so the problem actually exists). It's just that your proposed solution is not going to solve the problem. Instead, I even think it will worsen the situation. You seem to be over estimating the uniqueness humans have. Humans are not that unpredictable. Some human-only problems are considered solved by pattern recognitions algorithms. I also think that humans are more predictable than PRNGs. So why not incorporate a seeded PRNG into your hashing function instead? Such seeded PRNGs are less predictable than humans aver all.