It works! After a total of 14 days running purely from the capacitor, I have verified the memory contents to be entirely intact. The module was left unplugged on the bench for the duration of the test, with no special attempt to insulate it from RF, magnetic or other noise sources. In fact, it was a few inches away from a display with a noisy power supply, and within about 3 feet of an unshielded 300 watt induction heater. This suggests that the pull up/down resistors used are the right value to protect against noise.

Here is a final graph of the voltage over time: