Yesterday I was shooting my 50# Super Kodiak at 70 yards (aiming with the point) with arrows from two sets. One set (5) weighed around 580 grains, and the other set (2) weighed around 670 grains. Theory tells us that the heavier arrows would drop out first. They didn't, in several trials. 5 of 7 in my last group would have fit in the mouth of a 5 gallon bucket. One of each set was outside the group, low.
That has nothing to do with the subject at hand, but it shows you where theory can lead...
I remember reading about a similar FOC test from "Archery- The Technical Side". An aluminum arrow was made with a sliding weight, and no fletching. It was shot with the weight in different positions from extreme foc to reverse foc (boc?). As long as the weight was at the middle or forward, it seemed to make no difference in cast. Too far back and it would tumble. Drag was the same, since it was the same arrow. This test could be done in a similar fashion using a finished aluminum arrow with a positionable weight inside it, to eliminate the variable of having two different arrows with different fletching, points, etc.
I might try it, but I don't have any tubular arrows.