"But that is a red herring, I think."
Um. Yes, but no. Nobody is operating DC-3 aircraft in the US market, as passenger planes, because they fly so damn slow. You can't pay the pilots, and turn the aircraft around fast enough to book enough passengers per day, and pay the people who sit at the gate and take tickets, etc. etc. to make that aircraft pay for itself. Even though its MPG is pretty darn good, you just can't save enough money on gas to justify the slower flight speed. Or at least, you used to not be able to. A DC-3 works if you are hauling something that 'absolutely positively doesn't have to be there overnight, and you fly from deserted airfields... Or make mutliple short hops (skydiver aircraft).
Within a narrow range of flight speeds, say 500 to 600 mph, fuel efficiency matters, for current airliners. Drop much below 500 mph, and you have a plane that only pays on short runs, where the speed difference is enough for people to justify flying vs. driving, but not enough to justify a jet. Turboprop commuter planes are filling this niche currently. But in places where high-speed rail has become available, short-flight prop planes have seen drops in passenger volume.
"A heavier but more efficient engine offsets its weight penalty by requiring less fuel for a given range."
Well, it can, if the range is long enough and the weight of fuel great enough. Agree with your second statement.