~Later, my wife noticed it was rinsing with hot water.
Does the water eventually run cold? Perhaps the perceived temp of the water is what is in the pipes?
What do you get for wash temps at each setting (i.e. hot, warm, cold)?
I wonder if there is an outside possiblity that the water-fill solenoids hot and cold lead ("feed") wires are reversed right from the factory.
One other idea: Is there anything allowing hot and cold water in the pipes to mix and "cross-over" one into the other?
1- A portable washer with a "Y" connector set to receive warm water from a faucet?
2- A shower or tub set for warm water, but where the water is actually turned off by one of those water-saving shower heads right at the shower-head?
3- Do you have one of those devices/pumps that circulates the hot water (sometimes through a cold pipe) to keep the water in the hot pipes hot?
4- Is there a (mechanical)thermostatic mixing valve somewhere? Somtimes these are used to temper (dumb-down) the temperture of the water coming out of the hot water heater. Hottest water for one purpose, cooler water for say taps. This mixes super hot wwith tap cold to get a more moderate hot temp. Worse comes to worse you may have to put a check valve on the cold water line that goes into you hot water heater. [But this may not fix the propblem]. But it also won't stop any water-hammer that's for sure! This will also cause the need for an expansion tank on the hot water heater.
Should be interesting to see what this turns out to be.