The origin of the phrase "Now then!"

I think the fastest way to render the phrase intelligible is to punctuate it: "Now, then:", which I interpret as follows. It means, as you say, "We are moving to the next topic", which you could also say "Now we will proceed", so at least the presence of now makes sense. The then which you see as contradictory is actually not the version of "then" that means the opposite of "now", but rather, is therefore. It implies that what follows is a logical consequence of what was immediately preceding. The phrase now then seems to me to be used most often in some kind of monologue (a lecture or presentation) as a transition between motivation and application, as in:

Mike Lynd has suggested that the phrase is self-contradictory, but that is because of the existence of two unrelated meanings of the word "then". Now, then, I will explain how the other meaning makes more sense.

As you see (hopefully), the last sentence really only exists because the first one set it up. Then has functioned not as a temporal connector but a logical one.

The word “then” often serves a non-temporal function and introduces a consequence, as in the familiar sequence if…then: “If Socrates were really mortal, then he is probably dead.” So it is in this case: “Now, then,” means, “Now, as a consequence…” and generally follows a prior statement which the speaker wishes to draw towards its conclusion.