All else being equal, your intuition is correct that a larger aircraft will be more efficient (in a gallons per seat-mile measure) than a smaller aircraft. That's why there are big aircraft like 747's, 777's, and the A-380 flying on routes that have enough traffic to support them. When you have 300 passengers, it's more efficient to put them into one aircraft that holds that many than into two 737's to fly them the same distance.
Similarly, when all else is held constant, it's more efficient to go slowly than to go fast... how much effort does it take to pedal your bike at 5 mph vs at 20 mph? If you don't have the stopping and starting of city driving, your car will get better mileage at 30 mph than at 70 mph (assuming the transmission keeps the engine in an efficient range at both speeds) -- you're spending less energy overcoming wind resistance.
And the same "all else held equal" statement can be made about heavier vs lighter aircraft. For the same aircraft at the same speed & the same altitude (and winds, and temperature, and etc), the heavier one will use more gas to get where it's going.
The problem with the computations is that all three of these variables are changing when hopping between the Rutan EZ to a Cherokee 6 to a Caravan... speed is changing, the aircraft weight is changing, and capacity is changing. When all of these are changing, it's no longer a case of "all else being equal" and it's no longer valid to draw conclusions about the relationship of one of the variables (capacity, in this case) to efficiency.
If the comparison were between a Cherokee 6 and a 4-seat Cherokee cruising at the same speed, then you'd see results matching intuition.
Put another way, the fact that a 2-seat moped is more efficient (in gal/person-mile) than a 4-seat sedan is, doesn't mean that a 60-seat bus won't be more efficient than the sedan; it means that everything else that changed going from the moped to the sedan, obliterating the "all else being equal" assumption, overwhelms the inherent efficiency of the bigger vehicle. And, in many cases, we happily accept the increased person-mile costs of the sedan, since it is faster & safer & a more pleasant ride than the moped.
Same deal with the Caravan... it's faster, it's more powerful, it's a lot of things that make it more desirable than the Cherokee, and those not-all-else-being-equal factors make it look less efficient in this case. But that's more indicative of the distinct nature of the two aircraft, than information about the general trend of more seats making for better efficiency.
(Also, unless fuel were your only cost -- pilots & maintenance are free -- you wouldn't use 3 Cherokee flights to move the 14 people... all the other costs would make the Caravan a better deal financially, even if speed weren't a factor in the decision.)