Santiago would not be equivalent to James; you're right, that would be "heavy handed." Iago by itself would be equivalent, though. So Susan James would be Susan Iago, and Susan St. James would be Susan Santiago (santo iago; sant iago).
Diego makes it even worse to understand, because the "D" in Diego really and properly belongs to the word San, as a "t". In the USA we are so used to the Californian names of San Francisco, San Rafael, San Bernadino for "Saint" Francis, etc., that we naturally presume, with a city named San Diego, there was a Saint Diego. See, though, if you follow suit with San Francisco, you'd have San Iego (Iago/Yakob/Iacom/James). Its a mess, and nobody bothers, and you're not going to be able to formally change a city name (well, you can, but not usually one with 1.3 million people in it), AND in the meantime since consonants got pushed around over the last couple centuries, there's probably been somebody out there given the inaccurate name "Diego" who actually received sainthood!
As an humorous aside, if all that was done in making San Diego's name etymologically correct was to move the "D" (the soft "t") back to the word for saint, it would come out as Sand Iego, and folks would just presume the city name referred to something unique about their nice beaches.