Could a rotor head wing be plausible?
There is no need to attach the wing to the rotor head - simply attach it to the top of the fuselage. You could run the rotor through a hollow tube and attach the wings to that - the inner uncovered section of the wing is an interesting idea.

If you are looking for VTOL, a tilt rotor with two electric motors driven by the gas turbine may be a better option.