My last few trips I've noticed the cambio by the roundabout had the slightly higher exchange. Good for me since that's closer. I pretty much have given up at the one near Bourbon Beach... often w/out J$.
BTW... the reason you don't have to use ID is if you're in the computer system &/or they recognize you as a familiar face, not necessary. There have been times I started to present an ID & was told they didn't need to see it.