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"The 1-4% ancestry is based upon markers and does not denote a 1-4% genetic difference between humans and neanderthals. Neither is the genetic or genomic difference between human populations and between human and neanderthals the same amount of difference, but five times less."

Seems to me you're working overtime to emphasize that our DNA "glasses" are one-tenth of one percent empty.
I'm simply pointing to the fact: the DNA-glass is 99.9% "full" of identical DNA base-pairs.

You say there are five times more differences in genetic markers between humans and Neanderthals than amongst humans.
I'm only pointing out that the numbers of base-pair differences -- 3 million out of 3 billion total -- is the same between humans and Neanderthals as it is amongst various humans.

And I'm not disputing your time-line of divergences at all.
Clearly Neanderthals were more distantly related than our more recent out-of-Africa ancestors.

The issue here is: how "human" were Neanderthals?
Answer: plenty human -- human enough to:

Share 99.9% identical DNA base pairs.
Interbreed to the point of sharing 1% to 4% of genetic markers indicating common ancestry with Euro-Asians.
Possibly even to have passed on to Europeans and Asians cold-weather related physical adaptions essential for survival up north.

So even if Neanderthals were not our human "brothers," they still were genetic cousins, and, so it appears, kissing cousins at that. ;-)

I think “Cousins” and even “kissing Cousins” is about the right relationship.

Just as coyotes and wolves would be ‘cousin’ species, although more distantly related.

And it is not five times more difference just in genetic markers, it would be, overall, about five times more differences over all the DNA of the genome.

If the absolute difference in DNA of the genome among humans was 3 million out of 3 billion total base pairs, you would expect, when comparing humans and neanderthals, around 9-15 million base pair differences out of that 3 billion, not the same 3 million.

It is the total amount of differences in the genome, or via comparison of neutral genetic regions, that one derives that the time line of divergence, one that (in this case) agrees nicely with the fossil record.

If there were the same number of base pair differences, it would imply an equal time of divergence. But the amount of difference between a human genome and a neanderthal genome should be three to five times more than the amount of difference between any two human’s genome, which would indicate their divergence around five times longer ago (less than 100,000 years ago, compared to some 500,000 years ago).