If we have enough tests that look plausibly useful, each somewhat independent-looking, we could see how well they correlate. Test items on which good performance predicts high scores on other test items would seem more credible as indicators of actual rationality.

We could include behavioral measures of success, such as those suggested by Marshall, in our list of test items. (Income, self-reported happiness, having stable, positive relationships, managing to exercise regularly or to keep resolutions, probabilistic predictions for the situation you'll be in next year (future accomplishments, self-reported happiness at future times, etc.; coupled with actual reports next year on your situation) in our list of test items. If we can find pen-and-paper test items that correlate both with behavioral measures of success and with other plausibly rationality-related pen-and-paper test items, after controlling for IQ, I'll say we've won.