According to toller :

As was mentioned just turn the power off when you are not going to be
there.

My wife always starts the dishwasher just before we leave, so as to not
waste the remaining hot water, so we kinda need the power. I can't have my
cake and eat it too; maybe turning off the power (or at least the well) is
better than saving a little electricity/hot water.

I'd persuade the wife to run the dishwasher before leaving. Kill the
power to the HWT when she starts it.

When the dishwasher cycle ends, turn off the water feed to the HWT.

I'm not fond of killing power to the pump - you might lose prime.

There are filter on it now, but the water heater is apparently still full of
old debris that no amount of flushing seems to eliminate completely.

Drain HWT. Remove the lower heating element. Tape a short length of
garden hose (or whatever will just fit into the heating element port)
on the end of a shopvac hose, insert into HWT and suck it out.

Works quite well.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.