I don't normally like to jump on when there's already a pile of other posters, but in this case I think everyone else has overlooked a fundamental misunderstanding:
That asked, the chances of the mutations required between human and primate, occurring in the right gene and often enough in the population to change the genome of the entire species, are next to naught.
A specific mutation doesn't need to happen often to become characteristic of a species. It only needs to happen once. It can then spread throughout the population by inheritance.
If it's an advantageous mutation, then it's likely to spread much more quickly than if not. When we talk about an advantageous mutation, all we really mean is one whose possessors are liable to leave more children in the next generation than those without. So each successive generation a higher proportion of the population will possess this mutated form of the gene; even though the mutation only happened once.
Humans share two main anatomical similarities with apes compared to monkeys and apes which share nine.
I've seen you say this before, but am confused. Why do you consider these 11 characters to be of so much more weight than thousands of others we could pick from? Especially since you include a fairly obscure piece of skeletal anatomy in there. This seems very odd, since if you take into account all the rest of the skeletal anatomy humans clearly group with apes. It's not until the advent of molecular biology that the idea chimps were more closely related to humans than orangutans became widely accepted; but the grouping of humans and apes to the exclusion of monkeys predates Darwin.
But as a skeletal plan, all are mammals with forward vision and a collar bone. That's about all that's shared.
yes I would categorise primates as mammals with a collar bone, and forward pointing eyes
This has been bothering me so I could not resist returning to it. From where did you get this odd diagnosis of Primates? If it's your own work I'd suggest some more comparative anatomy is needed.
I thought it was odd before since ignores most of the diagnostic features of primates, including the obvious, famous ones that non-anatomists (like me) can easily understand (like nails). It's bothering me now since when you think about it doesn't even distinguish primates from close relatives. 'Mammal with forward-facing eyes and a collarbone' would be an accurate description of a rat, wouldn't it?