Any way to 'migrate' a Time Machine external for use with CCC? I have an external which I'm using with Time Machine, and I'd like to 'migrate' it and start using just CCC (Carbon Copy Cloner).

Is there a good way to essentially mv the contents of LatestTM to the root of the drive, and then have CCC take over from there?
I'm concerned about permissions and symlinks being handled correctly.

(It's over 1TB of data so I'd love to avoid re-copying everything.)
No, there is no way. Time Machine uses Symbolic links to previous backups when it hasn't changed. You could use some form of ls -H combination with xargs to copy the latest backup some what safely, however, some times those symlinks are broken. 

Furthermore, CCC won't accept that, because it also need to record which files it has copied, so in future it knows which are changed etc. You would be better off using a removing TM completely, format the disk, or create a partition for CCC. Though no point in keeping two backups on one external HDD, as both will be lost if it's destroyed.

CCC is very fast, it's not as slow as TM, so it shouldn't take long, as long as HDD has USB 3.0 (true, if inside of plug USB is blue). I was in the same place as you, where I didn't want to give up my previous back ups of TM. So ended using both, Time Machine to store all data, and CCC to create a bootable external copy of my disk. CCC only backs up the essentials, while TM does everything. When my PC's SDD is no longer functioning, I can boot up from CCC, and use TM to retrieve required data on the bootable.