How to achieve analog zero-drift sample and hold for hours?
Well, there seem to be solutions, although it's a bit of a blast from the past...

A Survey of Analog Memory Devices (from 1962)

"The transpolarizer, an electrostatic analog of the more widely known transfiuxor..."



For a more modern solution, a micro with ADC and DAC seems the way to go. Also, unlike the analog solutions, it is much more likely to be stable with temperature, which is always a nice bonus...

About large caps: there are several problems.


Capacitor value depends on temperature, thus with a constant amount of charge in your cap, the voltage will vary with temperature. The effect will be tiny, or huge, depending on cap type.
Capacitor leakage depends a lot on temperature (for electrolytics)
X7R is a piezoelectric microphone.
Dielectric absorption means that you charge your cap, then disconnect it, wait a bit, and then the voltage on it is now different! And it depends on the voltage that was there before you charged (or discharged it). Also, for large caps intended for supply decoupling, the effect is absolutely harmless, so no-one cares about it, and therefore there is no specification. I don't know if it depends on temperature and aging but there is no reason why it would not. You will only get a useful specification for caps that are intended for high precision integrators and stuff like that.


I remember measuring leakage on a 470µF 6V3 Panasonic FR cap. I charged it to 5V for a few minutes, then measured it every few minutes. The voltage would drop quickly due to DA, then it stabilized at around 4V. I left the cap on a shelf for a week, and measured again. Calculated leakage was in the nanoamps, but you'd have to keep it at the target voltage for a while (like at least several hours if not days) in order to overcome dielectric absorption... so it would be completely useless in this application.