I had not seen this list before. It is very useful. I believe that Obama was eligible in spite of his fraudulent birth certificate. He was trying to conceal another crime, not his birth status. Born in Hawaii to a U.S. Citizen mother. End of story.
Citing Wo Kim Ark and, especially, Minor v. Happersett doomed most of these cases. Those are poor choices upon which to hang your hat.
It would have been great if either House of Congress had subpoenaed Obamas original, vault copy, long form birth certificate from the state of Hawaii. Under the laws of that state an original birth certificate can be released to A person whose right to inspect or obtain a certified copy of the (birth) record is established by an order of a court of competent jurisdiction; An investigative committee of Congress would have qualified for such a court order. But Congress was not interested.