Thanks for the response, Marc. Since my posting, we've learned that the Aqua Therm is served by our tankless water heater and that it is a closed system, so likely not the cause of the smell. Our potable water is served by electric water heaters which do not sit unused.
We do have a high loop with the dishwasher, so we don't think that's the cause. We've had multiple plumbers look at that. The mystery continues