[dankruss]

I think it's important to first know which traits you deem to be 'culturally fit'.

Before coming up with a solution, the first step should always be defining the problem.

This could be worth running a workshop with the people you know are good cultural fits to come up with this trait-list.

In an interview (real-world application), similar to Google's layover test, I would suggest randomly picking people in the office to have an informal (but guided) chat around interests and everything after the fact of the candidate being competent enough to actually do the work.

As soon as that meeting concludes, send a form to all employees in that interview to rate against the traits you've defined.

Come up with a score tactic, if you want, and anything above, let's say 85%, is a fit.

Side note: You can be specific in your choice of words in the job posting to make it more likely that you attract the right type of people.