Well without the EU there are no examples to cite, but you state that no Jedi survived the purge, no records remain intact. You're suggesting that a literally galaxy-wide organization going back thousands of years has been erased in the span of a few decades. That a group of psychic, precognizant sentients was unable to hide material or people where they would be safe from harm. As Leia said in A New Hope, "the more you tighten your fingers, the more will slip through your grasp." Or was it tighten grasp and slip through fingers? Bah, been a decade since I watched ANH. EU Grand Admiral Pellaeon had a similar opinion expressed in Force Heretic I: Remnant.
Then we have Luke's little quest. He's taking one Nebulon-b, not even enough to be called a task force, into a largely hostile galaxy, and he's looking for Jedi secrets instead of students to train. EU and movies agree that finding Force Sensitives ain't easy, and his death would be a devastating loss to Republic morale. Farmboy's got more sense than that -- you go in hard or you go in quiet, you don't try to split the difference.