Odor originating from the hot water heater can affect the cold water but not on the widespread and ongoing basis that tummyman describes. Likewise, I would expect hydrogen sulfide generated by an electrolytic reaction stemming from direct contact between dissimilar metals to generally be somewhat more localized.
Unfortunately this sounds like it's originating from sulfate reducing bacteria in his well as he suspects. I'm not aware of any way to permanently "fix" the problem. Short of replacing the well, the options are limited to treating the water as it comes into the house.
I'll attach a pretty good article out of Penn State Univ. that discusses various treatment options.
https://extension.psu.edu/hydrogen-s...in-water-wells