Here's another portion of the article which I found interesting:
"So how could people from the 500's through the 1100's have made accurate carvings of dinosaurs long before dinosaur fossils had been discovered?"
(1) Has carbon dating of the patina of the specific Ica stones in question confirmed that range of dates?
(2) How could they? How do we today produce accurate illustrations of dinosaur anatomy? After all, none of us today have seen a living dinosaur. So why couldn't the ancients carefully inspect the fossils and make drawings that conform to the fossils?
"Why did 1/3 of the more than 11,000 Ica burial stones depict dinosaurs or pterosaurs?"
Why do a huge percentage of animal books produced for children today depict dinosaurs rather than modern animals? Answer: Because people are fascinated by strange and monstrous animals that look nothing like the living animals we are used to seeing in our daily lives. Why was the movie Jurassic Park so filled with enormous dinosaurs and almost none of the "average" dinosaur species which were around the size of a sheep? Why do dinosaur movies rarely feature many of the ancient species of animals which were more similar to the animals we see today?
"Why did the carvings show people and dinosaurs interacting?"
Why does the art of ancient Greece show people interacting with satyrs, minotaurs, cyclopes, water nymphs, and other mythical creatures? I don't know of any scholars who assert that such art constitutes evidence that people observed such creatures in their daily lives. Do you? So I don't understand why you are treating Ica stones any differently from other ancient art---if indeed the particular stones we are talking about are truly ancient.
"It appears that dinosaurs must have been an important part of the native peoples lives."
Is that truly the most likely explanation?
Also, there's a lot of scholars out there who would absolutely love to make a name for themselves in the academy by publishing conclusive evidence indicating that some dinosaur species evolved in ways that their descendants were able to survive the ecological changes of ancient South America. (Indeed, it was a very big deal when scientists published evidence that modern birds are descendants of ancient dinosaurs. The academy loves nothing more than paradigm-shifting discoveries!)
You talked about important evidence being ignored. Do you think it possible that those who publish claims that dinosaurs lived contemporaneously with humans are ignoring contrary evidence? Are they focusing solely on carefully cherry-picked "long shot" possibilities? When they publish their ideas, are they presenting all of the evidence to the reader or just the cherry-picked items and hypotheses which suit their purposes?