> I find it necessary to invest substantial effort in calibrating a new question. Before I ask a candidate a new question, I try use it to mock interview at least 10 people I have worked closely with.

You could do that some process, with the interviewee.

It would be a great way to see how collaborative they are.

i.e. you say "I've never actually worked through this problem myself, so I don't know how deep the rabbit hole is, but let's give it a crack and see what we come up with together."

Sounds a lot more like real-life to me than a manufactured question you've already worked through to the nth degree.