First, I have a couple of webpages you ought to read:
Barry's Tire Tech - Rolling Resistance and Fuel Economy
Barry's Tire Tech - Followup on Rolling Resistance and Fuel Economy
With that as background, let's start with the van tire thing.
Those are the European equivalent of LT tires. They are built more or less out of the same type materials. So are trailer tires, so what I am about to write applies to them as well.
Because these tires carry a lot of load compared to their size (compared to passenger car tires), the tread rubber is much stiffer and has poorer hysteretic properties (heat generation due to internal friction). Now you may think that a stiffer tread rubber would be better for rolling resistance, but because an inflated tire's casing to sooooo much stiffer than the tread rubber, the tread rubber's stiffness hardly impacts the overall tire's stiffness - so the tread rubber's only influence on RR is the hysteretic properties, and for LT tires (and van, and trailer tires), that's much worse than for a passenger car tire.
Put another way, don't use LT tires, trailer tires, or van tires (European style) on a car.
Increased inflation pressure? Up to a point that improves fuel economy, but not only is there diminishing returns, there's a point where the contact patch becomes so small that there are traction issues in the wet. This point seems to be dependent on the road surfaces in the locale where the tire is operating, so it isn't the same everywhere.
Aerodynamics? If a tire is fully exposed to the oncoming air, like an F1 or Indy car, a tire's width would be important. But 3/4 of the tire is surrounded by the car body, so a tire's width doesn't have much influence on the overall aero drag - and is easily overwhelmed by such simple things as the improved RR due to the increase in width.
Increase in tire size? That seems to be a good thing relative to FE. About 2 steps seems to be what most cars can accommodate - so in the OP's case, going from 205/60R16 to 225/60R16 might be possible. That increase would effectively reduce the overall gearing of the car, and folks here have reported improvements due to that kind of change.
And this should be coupled with a careful selection of make and model of tire - one that meets the wear, traction, and RR needs of the owner.