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Your statements about Neanderthals are just wrong and don't help you. It's another case where you emotionally take the evidence you do like farther than it goes. Neanderthals may have contributed to the human gene pool. Even if they didn't, that they intergrade at one end of their development with Homo erectus from which they sprang and at the other end with modern humans is a clue, another dot to connect. They don't seem to have contributed to modern mitochondrial DNA but that's another question from nuclear DNA.

That means you go from Egaster (I) to Cro Mag (M). Trouble is, egaster's descendents forgot to leave any fossils within the last 100K ...

Here you bludgeon with bad reasoning. The size of your gap is maybe 55K, not 100K. There are non-neanderthal hominids in the Near East variously dated at 90-100K years ago. Cro-Magnon shows up 40-45K ago. In a five or so million-year history, a gap of this size in just the presumably mainline sequence is nothing given the granularity of the fossil record, yet you hide in it and trumpet your imagined success.

Bones are too easy to dispute, even among evos (ever read a book called "Bones of Contention"?)

There's more than one, but both/all are by creationists. The best known is by Lubenow and it can safely be termed crackpot. Tell me you're not getting your material from there.

I could get a series of horse, dear, pig, dog and ape skulls that could show them 'evolving' from horses to apes. I could get a bunch of monkey and ape skulls, all extant species, and show modern monkies 'evolving' into apes.

Repeatedly, you grasp at straws. Your counterexample series have more problems than you admit, especially the first one. You have fossil records for horses, ungulates, dogs, and apes. Both of your strawman series are contradicted by those records. The apes-to-human series is un-contradicted by other data. It is evidence for the best and only real hypothesis out there.

What you're really saying is "Anything but humans-from-apes!"

Neanderthals may have contributed to the human gene pool.

Science says otherwise. Three separate studies by three separate groups of scientists using three separate DNA specimens from three widely separate sites have determined otherwise. In addition, there are numerous examples of Neanderthals and humans living in close proximity with no mixed specimens found. So no, the above is garbage. As far as science goes they did not. It is only in the fantasies of evolutionists that such is a possibility.