Epic fail

The comparative studies that I saw didn't seem to take into account the manufacture and transport of dishwashers

That is much less significant than your other point...

and seemed to assume the normal way to handwash included running the water constantly or at least using a second sink full of hot water that had to be periodically re-warmed.

The energy required to create and transport a dishwasher is trivial compared to the energy consumed by washing dishes over its typical lifespan.