Hmm. Some off the top of my head:

• Look for studies that have recognized a certain bias, then use that information to come up with reasoning problems where the participants have to reach the correct answer without falling prey to the biases. Somewhat vulnerable to people studying to beat the test, though can potentially be defeated by creatively combining several different biases and applying them into new situations. Downside: coming up with lots of different scenarios where one may fall victim to biases is a lot of work. Perhaps come up with suitable computer games where success depends on avoiding biased behavior, and the scenarios can be automatically generated?
• Calibration tests. These could be auto-generated, drawing on a far wider field of information than the current ones.
• As the above two, but subjects are forced to write down their reasoning. This may be more helpful in making them reflect more on their reasoning, than for actual verification - somebody's train of thought can be very hard to interpet, since they'll never write down everything that influenced their decision.