Actually a WATER cooled 4 stroke would be more efficient than a two stroke. Spark ignition on gasoline.A water cooled engine may be hard to find. If you are allowed mods you could jacket the cylinder and head. Use a lightweight thermo siphon to move the water under its own thermal differential. A small aluminum radiator would be easy to fab and lightweight. This would minimize power used to provide cooling. Air fans consume power = higher fuel consumption. Another good choice would be a diesel for economy . The water cooling allows a better use of the engines ultimate power. Engines are most efficient at peak pressure. A governor would not be needed to regulate the output ,the generator should be sized to have the right output at full engine power. Use the smallest engine that will deliver the needed power wide open. If you can locate some neodymium rare earth magnets they would make an excellent rotating magnet ,some proper impedance coils on the stator would eliminate brush drag. You can use some low loss diodes to rectify the 3 phase AC if DC is required.

Just a few rambling thoughts. I'll stay tuned or you can PM me. Good Luck !