I feel the point shape is less critical than other factors for a high performance flight arrow. However, the ideal shape should resemble the rounded nose shape of a 747 jet airplane, but this may be a relatively small factor as long as it is nicely rounded over. Sharply pointed shapes work best for supersonic projectiles, which is far beyond the speeds of the fastest flight bows. One of the worst performing flight arrow shapes that I have experience with are arrows that have a very long needle-like sharp point.
I don't have a very good method to analyze the center of pressure with my Primitive flight arrows. I do a little better job of this with my non-Primitive footbow arrows, by observing how they sink and shoot underwater. I can do this with arrows made of carbon and stainless steel components, but not with an arrow made of Primitive materials.
Probably the best advice I can recommend is to mark all your flight arrows with a permanent serial number and keep a log of how the arrows perform with different bows and shooting conditions. I observed some interesting things when I started doing this. First, I found that I had two or three arrows that were consistently the longest flyers, even if shot from radically different bows using radically different shooting styles. For example, I have one or two arrows that I found were used to set records for Modern Longbows 35 & 50lb), English Longbows(35 & 50 lb), and Primitive bows (35 & 50lb). Second, the arrows that matched the classic Turkish flight arrow geometry with the maximum thickness in the rear 1/3rd of the arrow were never my best performers. I have better luck with this shape if shot backward with the point where the nock should be, and nock where the point should be. Third, my high FOC arrows fly very consistent, but have not been the farthest flyers for whatever reason. They do seem to drill a deeper hole in the ground, but that is about it. Fourth, it is very important to pay a lot of attention to the fletching. Thick turkey feathers are the equivalent air-brakes.
Alan