Well, regardless of where he was born, he was a US citizen at birth since his mother was a US citizen. We have no working definition of what a natural-born citizen is, so assumption that makes the most sense is it mean any one who was born a citizen and wasn't naturalized later. So he was a citizen at birth, regardless of whether he was born in Hawaii or not.
Then there's the fact that a COLB has been shown, on official government paper bearing government seals, but you argue that doesn't count because.... well it could be a forgery- Despite the state of Hawaii saying it's real.
And of course, there's newspaper announcements of his birth, but those don't count, because... ummm... I got nothing.
And of course, there's no evidence that he WAS born somewhere else, like travel records for his parents.
I say your movement is stupid, personally, for thinking a 9 month pregnant woman would travel to Africa to have a baby.