I think the most straightforward way to fix this is either to not save the chest's content as NBT, or to not allow Entangled Chests to be added into an entangled chest.

Summary:
Adding entangled chests into entangled chest may cause a huge NBT data to be stored inside. Maybe a config which prohibits entangled chests to be added into it(so servers can disable it) might be an alternative

tbh, I crashed the world using Creative mode. In survival you would need to fill 27 different coded chests to the brim.
then somehow get 27 copies of these original 27 chests(you will have [27x27] worth of NBT), and then throw 27[27x27] chests into a chest.