No idea why the 6116 doesn't work, if it's plugged directly into socket, A10 is on 5V => high, thereby no floating pin, see no reason not to work.
Maybe it's too fast. I had that too, when I replaced the ROM with a new 70ns one. Old 150ns 27C512 worked fine though. The CXK5816 I use is a 150ns modell. Original Mk4118s are 200ns
My circuit:
Package of CXK5816 in schematic was just a part that matched the CXK5816 pinout, so just look at pin number and signal name.
Both MOSTEK 4118 /CS lines are put onto N-doped side of a diode. P-doped sides of diodes are connected together to /OE of CXK5816 and pulled high by 10k resistor. (simple AND gate)
So if both Mk4118 are disabled, both /CS are high, =>no current trough diodes => /OE of CXK5816 is high => CXK5816 disabled
If any of both Mk4118 /CS lines is pulled low, diode acts a 0 Ohm resistor (with a slight voltage offset caused by the PN junction, but still logic low) and pulls the /OE of the CXK5816 low, thus enabling the chip (need to disable it when reading data from ROM or IO).
Futhermore the /CS lines of the Mk4118 are connected to the theroretical MSB address line of the CXK5816 (practically you can use any address line, because mathematically the same, writes then to addresses mod 2, 4, 8, 16 etc.), thereby banking the memory. (Low address range 0-1KByte: /CS1=0 /CS0=1, High address range 1-2KByte: /CS1=1 /CS0=0)