I would also be skeptical of this theory - you say your hot water is worse than your cold - if it was your water source, it should be about the same.
Since you said you swapped hot water heaters, I’d be skeptical of the hot water heater. I’ve had a similar problem (mine was a sulfurous smell after not using the hot water for about a month) and you would still notice it in the cold water, but seemingly only because there was some lingering past the mixing valves etc.
Mine was mostly resolved by just running every hot water faucet in the house for about 30 minutes simultaneously. The idea is basically to try to “flush” your hot water heater and to try to “clean it out”. Might be worth a shot, as it’s not too hard and might help.