I think you're right about that, claire bear - as this page with various versions of the Columbia Pictures lady suggests. She does look a lot like she's based on the New York lady too.

My impression is however that Columbia as a personifcation of America has never really taken off, any more than Cousin Jonathan has. Never heard any songs about "The grand old dame Columbia" anyway.

(That Tenniel link you gave me crashed Internet Explorer for some reason...)