Sorry no heat sink nipples.
I just can't believe that debris in your heater could have blocked a 3/4" pipe. Nor can I accept that debris went to all of your faucets and clogged up every one.
Try visually following the hot water piping. There has to be something between the water heater and where the hot piping branches off to each bath and the kitchen that is blocked. Plumbers don't (shouldn't) put valves inside walls so you should be able to see any valve along the way.
In order to block all the faucets what ever it is has to be between the heater and where pipes branch off.