Center of Mass

If you look from a side view, when your car is slanted on the starting line, having the weight higher also moves it farther forward relative to the finish line. It does not fall farther being higher up either being in a fixed position on the car and the car starting at the same point even if you are just falling straight down. You are just shifting both the top and bottom of the fall up that much higher. Since the car isn't falling straight down but actually moving down a 27.1 degree slope you are actually making the fall time shorter since the weight is sitting farther forward the higher it sits on the car.
 
Sometimes it helps to draw out an exaggeration to help understand the problem.
First, imagine we have a magic car where we know we have a good stable car with the COG almost a 1/2 wheel in front of the back axle. We also have a magic weight that added no drag, and we can slide it up or down the orange line that represents the best position in front of the back axle. We will look at two extreme cases, a high COG and a low COG. Imagine the track is cut with a slot to allow our magic car to run on it with the COG way low.

cogmagiccar.jpg


We look at a typical Cub wood track that is more like the circular arc, but similar considerations with a best track apply.

coghigh-low.jpg


You speed is determined by how far your COG drops. Clearly more speed with lower COG.
 
pony express said:
The COG is one of the four tenents of pinewood derby building. ... I think some of the advantages of the lateral placement of the wheel weights is the ability to balance the rear lateral moment of inertia. It's like the tight rope walker. Would he rather carry a bowling ball or a long pole?

Regarding COG, I seem to now be paying more attention to the weight on the FDW rather than the COG for an initial setup. While the FDW weight does directly affect the COG front to back, but it also affects the COG side to side. In my limited experience, it is not just the COG that makes a car stable, but more of the weight on the FDW and just the overall weight placement in general. In my testing, lower seems to give a slightly better result.

When thinking of overall weight placement, it is interest what you said regarding the lateral placement of the wheel weights as well as lowering the weight location.