Hmm.. Although high Nitrate levels can kill fish over time, I don't think it would cause all your fish to die all of a sudden, even at the level yours is at. I've had Cardinal Tetras survive for an extended period in a tank with Nitrate over 200ppm. (long story, but the tetras are still as healthy as can be)
If you wash your filter this way all the time with no problems, then as you mentioned, it's probably not the cause, although I wouldn't recommend doing it anymore.
You say Ammonia and Nitrite show zero. Just to be on the safe side, you might want to make sure the kits are still good, and not expired.
Regarding the heater, if the heater did not electrocute the fish, might it be possible that the heater may have malfunctioned during the day, causing the tank to get extremely hot? This could have happened, and by the time you got home, it might have gotten unstuck and back to normal. Again, just an idea.
Finally you mention you haven't tested pH and KH yet recently. I think it'd be a good idea if you check. These can get lower over time, and if your KH dropped to a low enough level, you may have had a pH crash.
Other than that, can you think of anything else, however small, that might have been done differently yesterday that could have caused this today?
Before you tear everything down, I'd get the survivors out and see if you can pinpoint the cause, so that it doesn't happen again.
Oops, one more thing, just for our information, do you treat your waterchange water? (dechlorinate, etc)