Going from the cited examples alone, it seems that most of the diversity in answers may be caused not so much by "different intuitions", but vagueness of questions, as they can be interpreted in many different ways, effectively forcing the respondents to give answers to different questions selected more or less arbitrarily, starting from the vague statements of the questions. That is, the differing intuitions are not intuitions about properties of complicated situations being discussed, but intuitions about how vague words such as "knows" or "refers to" are to be interpreted in the given context.

A lot more tabooing might need to be done before such questionnaires can start indicating differences in intuition about substantive questions. Alternatively, thought experiments phrased as decision problems (such as the trolley problem) mostly avoid this issue, if they don't ask about characterizations of the situation other than the decision that is to be made (such as whether by throwing or not throwing the switch one becomes "responsible" for the deaths).