Herod's Dungeon would be a manual trigger by the newer definitions on triggers and conditions, which can be done any time the "blocking" condition is true but has to be activated manually. I would tend to agree that this can be played at any time on essentially the same level as dominants, and could also be triggered immediately as a response to finishing the block with Herod.
Based on this, and other, questions arising about when you can play dominants, perhaps it is time to revise the "at any time" description on dominants, to define when they can actually be played, and whether they have priority?