log_cdf not available in MultivariateNormalFullCovariance

In the distribution MultivariateNormalFullCovariance, the log_cdf is not available, because the event_shape is overriden. Is there an easy way to circumvent this? Why is this actually the case here?

Snippet to reproduce the issue (taken from the docs + added a log_cdf call:

from tensorflow_probability import distributions as tfd

b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape  # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape  # => [3, 1, 5, 2, 4]

x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.log_cdf(0.2)  # <- errors

Start by running the provided TensorFlow Probability snippet and tracing log_cdf on MultivariateNormalTriL and MultivariateNormalFullCovariance, focusing on the event_shape override mentioned in the report. Done means determining why log_cdf is unavailable and documenting or validating a supported way to handle the reported distribution behavior.