My son had this issue, last year, on two paired up water heaters, as almost exactly same conditions with the water softener, etc.............on a house they bought last year. He ordered two electric anode rods and we replaced both, from the top, as it's an easy fix. They stay plugged into an out let as it comes with a low voltage transformer, and a small diode green light stays on showing their working. Life expectancy is 5-8 yrs. on these things, as I'm good with that. Problem solved.
Good Luck,
HS 58
