A timer might help a little. Even with good insulation, it might turn on at 1AM
to keep the tank hot all night.
If you could keep it from coming on between 10 PM & 5 AM, you might save some money.
With super good insulation, the temperature isn't going to drop very low over night,
when no one is using hot water.. So, the 5AM turn on won't have to be a long cycle.
If you both work, does the hot water need to be on while you are both at work?
No one using it, temperature pretty stable.?. Turn it off between 8AM & 4PM..?.
IMHO, working people need a 7-day timer with a weekend program..
Mine is made for old retired folks..