Use Mini Tool Partition Home Edition Free and make a EXT4 partition on SD where the data will be moved. Now I don't know how it will work on Z1 but this is how it work on HD2, EXT4 will be used instead of Internal Storage. Let me know how it goes, I want do that too.
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My Evolution: Sony Xperia Z1 - UB + 4.3 Rooted + Deodexed, HTC HD2, HTC Diamond 2, HTC HD Blackstone, Nokia 7070 Prism, Qtek 9100, Nokia 3100, Motorola T720i, Nokia 3310, Sony Ericson PF 768 (Blue)
How Get Root on Sony Xperia Z1 with Locked Bootloader and the Latest Android 4.4