RE: I do have a question. With your experience on diodes, will the same 1 milliamp diode work equally well with a 24 volt power supply as with a 48 volt supply? Will it still limit the current to 1 milliamp with either supply voltage?
I would answer yes.
I have pushed 1 mAh diodes as high as 60v without issue. Though I'd add that there are limits to what a diode can withstand in terms of total wattage(V x A). And so it's important to outline this prior to experimentation. ie, as the conductivity of the cell increases, the voltage required to carry the amperage is reduced proportionally. Though I'd also add that the voltage must not fall bellow the minimum requirements for electrolysis. Otherwise, the electrolysis process will no longer work as intended.
RE: However I do take issue with this statement: "Though from what I can see, the problem of the constant voltage across the electrodes appears to remain."
Sorry for the confusion. The issue is not with constant voltage, but rather with variable voltage that could potentially fall under the minimum requirements for the electrolytic reaction.
RE: as the current goes up, the voltage across the electrodes must come down.
This is true, and I can see where the confusion could come from. ie, a voltage drop, and a drop in voltage(very confusing). That said, the difference between a resistor and /or potentiometer and a constant current circuit(for example), is where the potentiometer will lower the voltage along with the current(proportionate). Whereas a constant current regulator will only affect the current and not the voltage. Now I can see where this might lead to confusion as there is also a voltage drop across the electrodes under load. Though the difference here is that both the potentiometer and the load will have an effect on voltage. And so the conclusion is that the voltage has a greater potential of falling bellow the minimum requirements in this case. - to which I'd add, and to be fair, this is entirely speculative, as I have not done any formal testing to measure whether this is indeed the case or not.
Hope this helps.
PS. I might conduct a few tests between each of the circuit types this evening. - if so, I'll post my results