There is no aftermarket drive bay for thicker drives. Such a bay would not fit in the NUC (at least not without also (somehow) raising the height of the chassis).
USB 3.0 remains your best bet. It can transfer data at 5Gb/s, only 17% slower than the SATA III interface's 6Gb/s. Most of the prepackaged USB 3.0 drives use god-awful slow HDDs inside. Purchase your own fast media - best choice being a SSHD - and a USB 3.0 SATA III chassis separately. Remember too that you can use 3.5" media because you are external.
Hope this helps,
This message was posted on behalf of Intel Corporation
Thanks for your response. I will certainly investigate this as a good option.