Reel-Break ---
The NEC does not address all issues. In particular, since NM cables are not usually run in conduit and then into boxes, the code is silent on correct methods of fastening cables in your instance.
I often run 4 6-3 subpanel cables into main panels. I put a 2-1/2" piece of conduit into the main. Then I run the 6-3s and whatever other large cables I have into the 3" conduit and on into the main panel. The cables are fastened together outside of the conduit with zip ties.
This is sufficient to meet the intent of the code: to protect the NM cable outside of a box by ensuring that the sheath terminates inside of a box.