Firstly, id like to say good job and well done, i enjoyed this reading, and it presents a very possible perspective.
Secondly, i would like to contribute another source that might confirm this theory, this source is to be found in the religion of the early scandinavian people.
In general, Mythologies and early religions existed mainly to describe the things that could not be comprehended or explained at the time, that is why i believe that some confirmation to your claim that the scandinavian may in fact be some of the closest descendants to the Neanderthals, is within the early nordic mythology.
As all other mythologies of the time, there is a story describing the origin of the world and its inhabitants.
The Tale "Voluspa" Describes the creation of the world,
in the north lay the cold Niflheim, which consisted of tundras and frost, and in the south lay Muspelheim, a kingdom of fire and heat. Exactly as in the real world in the perspective of a person living in scandinavia.
Other than these kingdoms there was nothing but a cold empty chasm. Then came the first living creature, a Huge giant by the name "Ymer" and when he whent to sleep a jötunn son and a jötunn daughter grew from his armpit. The rest of his body contributed to creating the entire landscape, and also the "Gods".
From his hair came the woods. From his blood came the ocean. From his bones came the mountains. From his teeth came the sand and rocks.
Then his own creation Killed him when the gods, Odin, Vili and Vé, the Oldest gods of Nordic mythology turned against him.
I want to point out the Jötunn, are always described as a race that didnt live in Asgaard, but in Udgaard. As the gods lived in Asgaard. They are in all sources(prose Edda, poetic Edda, Voluspa, Heimskringla, Tyrfing and many others) described as stronger, bigger and more cunning than the normal humans who live in Midgaard.
The Voluspa Tale, ends with the destruction of the world.
The world will end with Ragnarok, a huge conflict in which all the beast in the world and the "Jötunns" will fight against the gods and the humans.
And according to the story, the humans will win, and start a new life in a new world.
What really makes gets me thinking here is this "Jötunn" people, i have never seen any mythology that empathizes so strongly on the different "tribes" of people. Normally, as in roman, greek, egyptian, zarathustra and others, there is One evil beast or person, or a handful. But never an entire Branch, living next to you.
Lets presume that these "Jötunns" where Neanderthals or close descendants of Neanderthals, they would look physically bigger and stronger, and with their slightly bigger brain capacity, we should presume that in some areas they would be smarter than the humans, maybe more cunning. If you didnt know why, you were so closesly related but yet so different with these strange humans that live a bit further down the river that you catch fist at, wouldnt that be something that you very strongly would want to have explained, for instance through religion?
Pressuming the forerunners to Nordic mythology was orally passed stories in families, that spread to tales and myths, untill they were written down in runes, which we dig up many years later.
What if scandinavian tribes intermingled with the Jötunns a long long time ago, even before the first nordic mythology sources, im not saying the entire scandinavian race is a cross bred of homo sapiens and Neanderthals but a lesser part might be.