How to manage Android's filesystem from a Mac?
As your device is rooted, you could try to install come SSHd app:


QuickSSHd explicitly mentions root support
DropBear SSH Server even requires it
SSHDroid mentions root as option


So all 3 of them should be able to "export" the full file system via SSH. So on a Mac (and Linux/Unix/BSD as well) you could directly connect from a terminal, or integrate the device's file system using e.g. SSHFS or Fish, on Windows you could use the famous WinSCP -- and probably many others.