You have found for yourself that it is not difficult to reduce water if you throw a suitably overwhelming number of electrons at it, but you're also skeptical that this reflects realistic experimental conditions. This means your physical intuition is working well!
The technique you are looking for is called constant potential DFT calculations, where -- precisely because you cannot trust what number of electrons you should throw into your system -- you control the work function of the electrode of interest, in effect choosing the electrode potential, and let the DFT package of choice use that to determine how many electrons are in the system and thus how happy water is to be reduced.
(Note that DFT people like to call it "grand-canonical ensemble" DFT, or GCE-DFT for short, because it studies the grand canonical ensemble for electrons. I dislike the term personally because some DFT practitioners refer to implicit solvent DFT as using a grand canonical ensemble for solvent molecules, and that's one too many grand canonical things for my liking. But you should probably Google GCE-DFT and see what you find.)
I've been reading these papers to get a handle on the technique, so perhaps they will be helpful to you too:
https://aip.scitation.org/doi/full/10.1063/5.0138197 (fresh off the press!!)
and this link on one implementation (solvated jellium in GPAW):
All the best!