I don't get it, why would failureException block anything ? The unittest.TestCase API must remain the same anyway, but it could become just a wrapper towards external assertions.

For example :

class TestCase:

   assertEqual = wrap(assertions.assert_equal)

Where "wrap" for example is some kind of functools.partial() injecting into external assertions a parameter "failure_exception_class". Having all these external assertions take such a parameter (defaulting to AssertionError) would be a great plus for adaptability anyway.