Recirculating heat motor ... can it be quieted or bypassed (pic included)

Easily enough done.

That means: a) I buy a cheap timer & leave the three valves in the open position b) I have the timer go on, once a day (probably at 5am before anyone awakes). c) It goes on for, say, a half hour or an hour (or whatever). d) That will make the recirc pump run for that half hour (or as long as it takes based on its thermostat settings).

The bacteria don't get a nice home to live in.

Legionnaires disease? Say what? If a circulation system was necessary to prevent legionnaires disease, hundreds of millions of home around the world would be having incidences of the disease. Only a tiny percentage of domestic hot water systems have any circulation system. The only advice I've heard in that regard is that the TANK should be heated to min of 130F.

I'm going to put the timer in, but not for the hot water.

It turns out the system actually seems to 'cool' the water (as explained prior) because it mixes up the tank. That, of course, probably gives more evenly heated water - but everyone has agreed the water appears hotter (much hotter) simply by disconnecting the recirculation pump.

The reason I'll put the timer in place is to keep the legionella down.

I understand.

I will put the timer in, set to run once a day.

I don't know if the lung-loving legionella would/could grow in the pipes when they're not circulating (I thought they like air conditioning systems), but it seems like cheap insurance against them.

Especially as they can't be seen and I wouldn't have any way of identifying the bacterium in the water supply.

You got your flow direction backwards. The pump on such "instant" hot water systems returns water to a T plumbed in with the drain spigot at the bottom of the water heater. ^_^

TDD