Using an airship shape as a fuselage by adding rigid of flexible wings on the sides could perhaps lead to more scalability. A preliminary sketch was attempted.
The fuselage could be shaped like the currently longest airship (124 m)
Perhaps a fuselage can be made in light (50-90 g/m²) aluminised fabric or specific insulating fabric, in order to keep heat enough from the central heating cable, with a reasonable energy expense. Indeed the bigger the balloon, the less energy expenditure (Watt per Newton lifted, W / N) because the losses by convection only increase with the square.
If the construction is really light, a few degrees are enough to compensate for the mass of the whole, provided that the fuselage is really enormous. The less temperature rise there is, the more insulation problems are reduced.
If balance is approximately achieved, takeoff and landing operations would be reduced to those imposed by storms or thunderstorms.
Moreover an aerodynamic form like that of airship shaped fuselage could be more efficient (less drag, better glide ratio, better stability with wings?) than fat designs mentioned also in the initial comment, or chubby designs.
The whole AWES could be a static one (flygen), or a crosswind one with both flygen to supply the electricity for the heating cable and yo-yo mode, or fully flygen.