I've read the Z2 manual, and got to the screen that says in effect it's ready to have the address book transferred over, but I can't figure it out how to do it on my iPhone. Can anyone help here?

You can try searching the forum next time, there you will see several post indicating that its not possible to transfer untill Apple updates the BT contact profile. It can only be done with devices that can pull the info from the phone, Pio units can't do that.