Very well summed up.
In addition, same set of questions can also be asked to people who've recently left the organisation.
I'd use the following criteria to filter ex employees:
- Reliable 1st/2nd level connections
- Folks who have shown stability in the past (generally stick to jobs for > 2 years)
Obviously, they'd come with biases. But, talking 2-3 people should also help reliably gather broad culture patterns. Should avoid listening to evidently disgruntled folks.