Speaking of electric planes, I wonder what'd be the optimal specs if the only variable that we'd try to optimize was consumption (assuming a 1000 kg payload and 600 mile legs, unrestricted runway)?
The most fuel-efficient configuration would be one having a very high L/D. The best examples are modern sailplanes, aerodynamically clean, and with very long, slender wings.
To truly answer this question you would have to outline all the theories of aerospace engineering and explain how they interact with each other.
Everything on an aircraft is a trading game, you want more speed, you're probably going to have an aircraft that's hard to control at low speeds since the control surfaces can't be very large when facing extreme wind speeds..
However there are only 4 basic forces of flight. Thrust, Lift, Drag, and Weight. All the crazy designs we come up with in aviation is us trying to manipulate those 4 forces in a way that fits the desired results.
In almost all cases the idea is to maximize Thrust & Lift while reducing Drag and Weight.
You've already kind of locked in "Weight" at 1000KG. However 2 things also add to the weight. The structural weight of the aircraft, and the counter lift weight the real tail wing produces.
So our best airplane would be made out of some super space material that is as light as possible to avoid adding structural weight.
Also on most planes the tail wing produces downward force to stabilize the aircraft and provide stall recovery. However this isn't a requirement, with modern computers powering on the fly adjustments people have made flying wings.
This is really the best aerodynamic shape we have at maximizing lift/thrust ratios. The longer the span of a wing, the more efficient it is.
So basically your plane would be made out of space age composites, have a wing span as long as physically possible and a computer powered control system to keep it all aerodynamically stable without a tailwing.