Thank you for your thoughtful and clear article on an important subject.
http://autismtheory.org traces
why Neanderthal and Denisovan DNA probably correlates with autism to basic physical facts. The thesis, now over ten years old, is posted at the site in a paper titled
The Sparseness Adaptation Syndrome: Adaptation to low population density yields a set of traits correlated with autism and male gender.
Neanderthals and Denisovans lived in regions and habits of relatively low population density.
The paper is here:
http://autismtheory.org/sparse1.pdf