I wondered if the 100 Ohm resistor would be adequate current limiting when charging the dead cap.
It is probably a 1/4 watt resistor so I think it will be fine. It had to be designed to take into account a fully discharged or shorted NiCd battery and the supercapacitor will charge quickly.
If I went the Cr2032 or similar route then I would remove CR1133 to prevent charging the lithium cell, and perhaps stick a diode in with the cell as well in case there was some feeding from pin 13 of the CMOS through the 22K resistor. Might be cool to have two battery holders in parallel so a second cell could be inserted while changing the first. It is annoying to lose the cal data.
CR1133 is still needed because the SRAM has to be powered normally when in operation. The only change is adding a diode in series with the battery. The diode could replace R1131 but it is better to keep the series resistance as a safety measure.
I always thought the DM5010 memory backup time was too short for reliable operation. If I had one, I would probably change it just to fix that aspect of its operation.
As far as dual battery circuits, it would be almost as good to just be able to change the battery while the instrument is in operation.
Now I just need to find a source of 200Hz 190V and 700V AC for the calibration procedure. I think I can generator all the other input voltages, and check them with my Kiethley. These "modern" DMMs with the software calibration are a bit of a pain because you can't just use 120VAC, turn a pot, and say that is "good enough" for the 1000V scale. Instead they want specific voltages on their input.
Finding a calibrated AC or high voltage source is a perennial problem. Some instruments allow entering the actual applied calibration voltage as long as it is within a specified range.
Do you think the 3.6V of the long life battery you suggested would be an issue? (vs. the original 2.4V)
No, it will not be a problem. The SRAM drops into low power mode depending on its control signals and is quite happy anywhere between about 2 and 5 volts. A primary lithium cell would require a series diode anyway to prevent charging when normal power is applied so the 3.6 volts would be about 3.0 volts anyway. Your 3.0 volt lithium 2032 cell would become 2.4 volts.