So there's no way to override that setting using node_access? According to the handy dandy diagram on page 104 of 'Pro Drupal Development' it looks like node_access is the last thing checked when granting access to a node.  Is that incorrect, or am I misunderstanding how that process works?

Note that you only reach node_access if the results from hook_access() are inconclusive. In this case it's not inconclusive; project module is returning FALSE and therefore access is disallowed.