So far the results are much better than expected, the module has been storing data without external power for over ten days, and is still well above the cutoff voltage. Here is the graph of the voltage over time, with a comparison to a linear drop in voltage:

It looks like the RAM takes less current to run as the supply voltage drops. Even if the curve does not flatten out any more, the module should retain data for another two weeks, in addition to the ten days it has already run!

The one caveat here is that I haven't been able to check the memory contents since starting the test. Applying power to the chip to read the RAM would of course recharge the capacitor. So I have no idea if the memory has been corrupted by noise. I will probably wait a few more days before stopping the test to run verification, just to bring the run time up to a nice even two weeks.