If you want to use the word "determinism" in that sense, then a far better definition would be "the voting outcome is not affected by anything other than the votes of the voters", which my system does hold to.

Fair enough, but it's not a matter of how I want to use the word "determinism". That word in Arrow's Theorem has a certain technical meaning, and your system does not qualify as deterministic under that technical meaning.

You're making the case that determinism, in Arrow's sense, is not such the desideratum that it's usually made out to be. FWIW, I'm coming around to your point there.