I'm out of my element dealing with Time Machine, itself, but just thinking, I wonder if your clone needs to be on a
separate partition on your backup drive?
So, even without an answer to that question, I'll suggest that you partition your new drive into (at least) two partitions and use one for Time Machine backups and the other for your clone; it should work for you, and it most assuredly won't hurt. (
Partition a Drive with OS X El Capitan's Disk Utility)
More: I believe you can partition your drive even after having backed up to it without losing any data, but that'll have to be confirmed by someone else.
