In fairness, I've seen precious little actual experimental evaluation of just about any of our CP calculations, not just the base drag hack. We really need an army of high school students doing science fair projects with wind tunnels.THE BASE DRAG HACK DOESN'T WORK IN THIS CASE, JUST LIKE THE BASE DRAG HACK DOESN'T WORK IN A LOT OF CASES. We have no real reason to believe the base drag hack ever works right. As far as I can tell no one has ever done a careful comparison of a measured CP vs a CP calculated with the base drag hack. Ever. For any design at all.
I am curious why you are asserting the hack doesn't work in this case, however. As I understand the aerodynamics of the pyramid, and the base drag hack, it seems like it ought to work fine.