Best Method to Backup Data from No Root Recall Tablet ( Locked Bootloader) to new one

As it says in the subject line, I'd never felt compelled to root my Shield Tablet buy now wishing I had. It is on the latest 5.1.1 update and I want to transfer my data in such a way as go clone it onto the new tablet I've received due to the recall.

Is there anyway of making a Nandroid backup and loading recovery without unlocking and losing the data I want to keep or another alternative method such as the built in adb backup solution.

Thanks for the assistance in advance.