Am I reading it right?
Yes, with the exception of one clause -
may carry in any State a concealed firearm in accordance with the terms of the license or with the laws of the State of the person's residence, subject to the laws of the State in which the firearm is carried concerning specific types of locations in which firearms may not be carried.'
Prohibited locations stay prohibited according the laws of the given state. I say it's an interesting experiment - while I'd like to see the power of the states come through on reciprocity, I wouldn't do much complaining if this was passed as written.