I've finally put together a working prototype cartridge for my GameTank system that adds battery-backed SRAM so programs can save persistent data.

This board has 32Kbyte of RAM in addition to the 2Mbyte Flash of my previous design. As before, a shift register is used to select the higher-value address bits of the flash memory. One of the shift register's output pins was unused, so now it selects between the Flash and the SRAM. Also as before, any accesses to the upper quarter of memory will go to the same window in Flash regardless of the shift register state. This guarantees that the Reset vector is accessible on boot.

So far the prototype performs well, and can save values between game sessions while the system is powered off and the cartridge is removed. There currently isn't any protection against the RAM getting written during undefined cold boot behavior, but this only seems to affect the bottom address of SRAM.

One curious behavior happens while the system is powered "off" but the cartridge is not removed. Some of the RAM chips partially retain their contents, for many hours at least. I got the multimeter out and found that there is indeed about 1.5V on the cartridge power pins.
I'm still learning the analog domain, so I'm not sure whether it's to be expected from this design, if I picked the wrong diodes, or if this is particularly harmful to the system. It's possible the best solution is to put a note on the back of the cartridge indicating the battery will last longer if the cartridge is stored outside the system.

It could be due to the pull up resistors on the CS, OE, WE lines of the battery backed RAM. You don't specify what the values of those are. When the cartridge is plugged in, those lines are connected to something on your main system. It's possible that power is being applied from the back up battery via these pull up resistors and protection diodes on chips on your main board. It's worth investigating further because you might find the back up battery runs out quickly if the cartridge is left plugged in to a powered off system.

Good point. The resistors are 3.3K but maybe some extra diodes are in order for these.