Why has our nose evolved with the nostrils facing down?
I have not been able to find any studies that look specifically at the genetic mechanism for nose development. I certainly do not know but I'll offer up two hypotheses. 

My first hypothesis is that the elongated nose is a remnant of the elongated lower face of our ancestral species, as you note in your answer. Take a look at this brief YouTube video (1:17 long, the part relevant to this answer begins at 33 seconds) of a time-lapse composite showing the develop of the human face. Our face develops as two separate halves that meet together in the middle. That's what creates the philtrum under our nose. 

Watch the especially carefully from the 54 second mark to 1 minute mark. Note that our nostrils are pointing directly forward and the overall region looks somewhat like a pig snout. The mouth is vertical aligned with the front of the nose. The overall face is much more rectangular and the eyes are on the sides of the face.

Then, the face begins to become rounder and flatten. The eyes move to the front of the face and the recesses our our eye sockets recede. The lower face below the nose recedes, becoming flatter. The only part that does not recede is the nose area. The flattening of the lower face may actually cause the nostrils to turn downward.  Our nose does not develop outward from a flat face but instead is left behind as the rest of the face flattens.  This would be my initial thought as the primary reason for the shape of the nose and direction of the nostrils.

My second hypothesis (and honestly independent of the comment by @Remib) is related to our sense of smell and taste. Although our ability to detect flavors is a complex process, the primary sense involved is smell (Shepherd 2006). Therefore, downward-pointing nostrils are located directly above the mouth so we get a good smell of the food just before it enters the mouth, perhaps enhancing our flavor-sensing ability.


  Shephered, G.M. 2006. Smell images and the flavour system in the human brain. Nature 444: 316-321.


Note that these two hypotheses are not mutually exclusive. The downward pointing nostrils may be a remnant of our facial development but provides an (adaptive?) advantage for flavour perception.