I don't know about Inca astronomy, but if it's anything like Mayan astronomy it's going to be pretty sophisticated. The Mayans did a far more involved and clever bit of astronomical story-telling than the Greeks. All their constellations are characters in their creation mythology, which is itself detailed and elaborate, but they went way beyond the Greeks by having the constellations positioned in sequence in right ascension along with the storyline in the Popul Vu. A Mayan priest can go out and tell the story of creation, pointing to the new characters rising in the east and explaining how they slay the characters setting the west, and he can do it for the full 360 degrees of rotation. They'd go out twice a year and spend all night to fully recount the stories. In a religion that was so all-encompassing that they'd carve out human hearts and wear the skins of their victims like cloaks, there was probably a lot of general interest in understanding the story in the sky.
Kewel! I'd like to read up on this, if you have a source reference?
Actually what you discribe the Maya doing is very much like what the early Greeks did do? Have you read "Homer's Secret Iliad" by Florence and Kenneth Wood? it describes this very story telling technigue, stars, contellations and all.