It now has 3 partitions for various backups, including bootable clones, Recovery HD, and other stuff.
As written, that doesn't sound correct.
You need one partition for Time Machine and another for your bootable clone. You don't need a partition for Recovery HD, because when you clone your HD to the external, CCC will ask if you want it to create a Recovery HD, and if you go for it, it will carve a new, invisible partition
out of the one on which the clone lives.