I do recognize that the Lagar Velho child is the subject of acrimonious debate. I don't really want to engage that acrimonious debate except to say that thus far I find the anti-hybrid arguments more persuasive. I have linked the primary argument in post #211 above.
And beyond that, I want to emphasize that what I am listing in post #175 are all the factors that in my view would ordinarily lead to a clear designation of Neanderthals as a distinct species (if they were just discovered today).
But as has been pointed out over and over (usually in dispute of my position!), distinct, but closely related, species can nonetheless in certain cases produce hybrids.
Can't find a link for it right now, but one theory I've seen is that the Caucasus Mountains and an Ice Age might have caused the isolation of the gene pools in the first place. Recall that high but normally passable mountains separate the Black Sea on the West and the Caspian to the east. It's a long way around the water barriers if for some reason you can't get over the mountains.
In this scenario, humanity expands north across the Caucasus only to have a population isolated there as Ice Age conditions close the passes. That's the birth of the cold-adapted Neanderthals.
It may be too specific for the available data.