I tried copying the SD card to a folder and then to the new card. I used Linux Mint 17 running Nemo as root. If you don't have Linux installed, I would recommend a Kali Live disc, since it runs as root.
Everything seems to have been copied, but the first boot of the phone gave me an inconsistent UID message. It was gone at second boot. Some apps worked, some worked after reinstalling, and others lost all of their data.
If you try this, move the stuff you really don't want to lose back to the phone. Starting a game all over again when you were at level 200 really bites. Facebook and Messenger store everything on servers, so they could be easily reinstalled.