We don't use places that ask for ID when exchanging money. I don't think you are but if by chance you are up here in Zona Norte let me know and I'll point you to where where we go.
For some reason my wife knows who asks for id and who doesn't and does not trust anyone that does. We were walking down the street in Belgrano one day and she said "let's go there, they don't ask for id".
I have a feeling you may be able to ask a friend who is a local and they may be able to point you in the right direction.