Assuming that the main priority is how the audience in the theatre experiences this number, and not how passers-by on the street might experience it, would it be so bad if this was done entirely indoors within a theatre building? Have Eva perform the song live in some backstage space designed to look like the Casa Rosada balcony, keep the camera pointed in the right direction to avoid giving the game away, whatever. Whatever commentary is intended about the song representing Eva putting on her public face, might then come across just as well to the theatre audience. Yes, it would all be "fake", but so are all the tricks and solutions that create theatrical effects in any production anyway. Presumably the moment should be more about the final theatrical effect produced, than the approach used to get it.