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.
How such a vehicle could carry 4 people is a mystery - let alone how it could carry the dog and a week's worth of groceries, or a trunkful of luggage. Those silly little electric bubblecars seen in Boulder and other "enlightened" places - they have too much wind resistance to make it. (And, they only have one occupant capacity.)
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.