I hear you and agree with most of what your saying. The only thing I disagree with is that the Incas sacrificed their virgins in the name of science. Before the fallout of World War II, eugenics was big science and strongly connected to Darwinism. Thanks to the Nazi experiment, there has been a big repentance on this. However, the very things that Timothy Birdnow brings up in his article about progressive science could be characterized as a soft form of eugenics. Eugenics as practices under the Nazis was the most extreme form of social engineering and social planning.
The Incas did not sacrifice virgins to ensure the sun continued to rise. I think several notions are being conflated here.
The Incas practiced human sacrifice, but to a much lesser extent than the Aztecs, Mayas and other Meso-American groups. These sacrifices were generally performed to celebrate important events such as the death of one Inca and the accession of the next, or to propitiate the gods in times of drought, war, etc.
The Incas primarily or exclusively sacrificed children, who I guess we can assume were virgins. They were generally buried alive on the peaks of high mountains.
I know of nothing to indicate the Inca thought this was necessary to ensure the sun came up the next day. That ideology was from the Aztecs, who believed the sun needed to be fed human life-force to strengthen him in his fight against the forces of evil. Most of those sacrificed for this purpose were prisoners of war, who we can assume were probably not virgins.
However, the Aztecs also sacrificed women, children and other groups for other purposes.