.
Thank you for asking, Neil. I bet you timed out on this one!
According to my principle, when it comes to number, rather than amount, none is never more than one. None is always less than one. Therefore it requires a singular verb.
The first example should read:
None of the US presidents is a woman. Not None of the US presidents are women, or is women.
So, yes they are all properly rendered with the singular verb, "is".
.
You wrote:
"None" is an abbreviated form of "not one".
.
Most of the time,
"not one" is more than one:
2,
3,
4, ... and so on, are each
"not one.".
Zero is the exception, not the rule.
.
How many passengers are on the ship when the ship is empty?
None are on the ship? or,
None is on the ship?.
How many of this farmer's tomatoes are rotten each day this time of year? None are rotten? or,
None is rotten?.
How many movies are rated G at this cinema? None are rated G? or,
None is rated G?.
How many of these are there? There are none of these? or,
There is none of these?.
So, then if the list of examples above are all right, including this one:
"None of these sentences is correct" ... (In answer to the question, "How many of these sentences are correct?") ... then
none of them are correct, because
them be incorrect!

.
.
PS -- I did not time out on this one!