Most of what you posted is correct except this. 120/240 has NOTHING to do with your electric bill. It MIGHT be possible in some cases that an "almost overloaded" "on the ragged edge" heavy 120V motor, like a compressor, might make a difference if you convert to 240, and it might not, either.
VA is VA, watts "is" watts and power is power.
Just because something is 240, does not necessarily make it more efficient.