Basically, the point is that "the secret" to a vehicle with 300 mpg mileage isn't in some sort of special internal combustion engine that is much better, but rather in realizing that such a vehicle would have to be lighter and have less wind resistance than a moped, if it were supposed to travel at 60 mph. You've actually been over-optomistic in your calculation: basically you've shown the power required for level ground; if you factor in the power requirement to maintain 60mph up any significant grade, the challenge becomes all the more difficult.
Essentially, it would take a vehicle made out of "Unobtanium," that mysterious material that is infinitely strong, infinitely light, and has infinite fatigue resistance, and isn't brittle. Even then, the hill climbing power requirement of the payload alone would take more than a lawn-mower engine.
Could all the unobtanium have been left on Saturn when the Earth was still ... how does that theory go?
Two adults weigh 300 lbs, and two kids another 150. The dog is 20 and the groceries are another 50. That's 520 lbs, or about 250 kg. If E = mgh, then raising them 1 m would be 250kg x 9.8m/s
2 ~10 = 2.5 kJ. Say 2.2 kJ to make the math easy. If the engine delivers 6.6 kW, then the entire power of 6.6 kW would raise them 3 m/s. Since 60 mph is about 27 m/s, which we can round to 30 m/s, then the entire power budget, in the absence of air resistance or any other kind of loss, and with perfect 100% efficiency, is that they could go up a 10% grade at full speed, but no steeper. In a vehicle that has zero mass - this is just the energy it takes to lift them, the dog, and the groceries.
The people who think there are 300 mpg vehicles must be the same ones who think that the oceans are rising, because the island of Tuvalu is sinking. But wait! Q: If the oceans are rising, why is only Tuvalu, but none of its neighbors, sinking? A: Because reality has nothing to do with the opinions and beliefs that these people hold.