I'm running 4.3 with the MJ5 bootloader and stock recovery. I have had success using saferoot to regain SuperSU and associated functionality back.
I had root with 4.1.2.
After 4.3, I sorta had partial root. Apps could be granted root, but I was unable to update SuperSU.
For me, I had to unroot the device and then use saferoot multiple times to eventually get a successful root with the latest SuperSU.
After all this, and even when I had partial root, ES File Explorer doesn't seem to be able to remount /system as RW on 4.3.
I haven't had any issue remounting /system as RW from a shell console on a PC via adb.
saferoot installed the latest SuperSU so I still don't know if I'll be able to update, but for now its current.
You can find info on saferoot here
best of luck,