"Alex, why is one blogger's transliteration more authoritative than that of Judaica Press?"
I am the blogger. It was not my transliteration, but a quotation. It was Israel Solomons' transliteration in his 1915 article on Haham Nieto.
The reason why his transliteration is more authoritative than Judaica Press (in this case) is because he was a historian and he knew how this particular Sephardic surname was spelled in Latin letters. You could ask the same thing about many names. For example, Haham Nieto's name is spelled "ניטו" in Hebrew. So how should you spell it in English? Well, as it happens I know that in the 18th century he signed his name as "Netto." For whatever reason it became the convention to spell it "Nieto," and this is how people of his family still spell the name. But some invented conjecture based on "ניטו" (such as, say, "Neeto" or "Naytu" or any of a number of guesses which people could make) would not be as good as "Netto" or "Nieto." Since the real name was the Spanish name, how he or anyone else decided to spell it in Hebrew cannot really inform how the name should be pronounced or spelled in Latin letters, unless the family became Israeli and changed the pronunciation of the name. Then in spelling their name you could make the case that the Israeli pronunciation should inform how it is to be spelled in English.
"Pidanki" is, first of all, Hebrew, because in Hebrew a word cannot begin with a Pheh. Since the name is Spanish, it begins with a Ph or an F.