I started this experiment attempting to create a low voltage non-toxic battery that would be easy to make and carry around. I may yet do this but for now I've created a capacitor, which is a electrical component used to store energy in an electric field. I chose to make the housing or shell out of hard candy because sugar heated to high temperatures takes on some of the properties of glass and is an easy insulator to create cheaply.
I've recorded capacitance tests of four of the cells wired in series and parallel as well as daily electrical potential over the course of two weeks
here.
I initially made molds by hollowing out potatoes, which could still be done, but I became frustrated with my design falling over and spilling the sugar syrup so I bought a silicon mold used to make ice cube shot glasses instead. Whatever you decide to use, oil all surfaces that will touch the sugar and set on a cutting board to allow for ease of movement.
Rochelle's salt is famous for being Piezoelectric, which means it deforms under an electric field. Likewise, it will release energy when it is deformed... this is the way quartz oscillators work in clocks (switching back and forth between electrical and mechanical energy) but it's not good at storing any useful amount of energy.
You were absolutely right about the hygroscopic nature of the salts, and that is very important here, but perhaps not in the way you think. The main thing here is conductivity, and I bet if you measure it you'll find the conductivity of your mix it very high. Capacitors work by separating charges and storing them on plates. The closer these plates are, the more energy they can store in their electric field, but the key to this is LOW conductivity (as close to zero as possible). These cannot work as capacitors.
The most important issue missed here is the use of 2 types of wire. Try it again with only one type of wire, and I'll bet you find it doesn't work. What you've actually made here ALMOST a battery. You have two metals of different redox potential in a conductive medium but there are 2 problems. The first problem with your battery is that aluminum has a natural oxide layer on the surface, which "passivates" it. The second problem is that both species are in their reduced (metallic) form. This is what you are changing when you "charge" your cell, forcing a small amount of copper metal to give up electrons (becoming oxidized) and turn into copper ions which stay nearby in your salt mix. Most likely , is it the sulfate being reduced to sulfite, or possibly the tartrate being converted to an aldehyde which allows this to happen in this system
To fix the first problem in a permanent way replace the aluminum with zinc. Tho fix the second one use copper sulfate instead of magnesium sulfate, and you will suddenly notice a BIG difference.