First off, how do you know the authorship and time frame of each of the OT books? You argue as if you have absolute knowledge, when I don't think anybody knows for sure the authorship of all the books.
Second, what is a "prophet?" Isn't it someone who speaks for God, delivers God's message to the world?
Then your argument is circular and self-defeating. If the authors of what you call the "Apocrypha" were truly inspired, then they were "prophets" and they obviously then lived during the "time of a prophet." It's tautological.
SD