Well, you asked for DUMB ideas, so here's mine. It has the advantage that I'm sure no one else will suggest it. This is based on an accidental discovery (so far as I know, unpublished) that one can compare two arbitrary documents for similarity (even if they are in different word-processor formats) by running them both through a recognizer built out of a random state machine and comparing bit masks of all the states traversed. The more common they are, the more states will be traversed in both.

So, lets assume we have a panel of highly rational individuals which are our control group. We generate a random multiple-choice questionnaire consisting of nonsensical questions and answers. Things like:

1) How Green is the Smell of Bacon?

a) 7.5

b) Neon

c) Introspection

d) Larger

You then do a correlation over how your panel of experts chose their answers and see if there is a common pattern. You then score students who take the test based on how similar to the common pattern they are.

Assuming this idea works at all, the advantage of this is that it would be extremely difficult to game. The disadvantage would be that it would penalize those who are significantly more rational than the 'norm'. It would probably also require the panel to be similar to each other in cognition. There is also the general problem of not knowing if you're really testing for what you think you're testing.

Frankly, I don't know if I'd be more happy if this was tested and shown to be workable, or if it turned out to be a really stupid idea.