A whole host of engineering problems would arise from trying to fit a turbine to an R-22.
The vertical CG would move up significantly - this will affect the lateral directional stability, as well as the longitudinal stability - the rotor mast is pretty high up to give good effect to the main rotor-CG relationship, and moving the CG higher isn't going to help.
With the CG moved higher, the sideslip might well give a negative dihedral effect (i.e. left pedal gives right roll).
Can the airframe take all that power? Good question, and I assume it could be solved by limiting the power output of the engine.
More to the point - the rotor will run out of ooomph at some point, regardless of how much power you put into it. Where will that happen? Since the engine would be flat rated and able to put out the maximum the transmission could take until you were nearly on the moon, people would think the rotor could do the same. Unfortunately, not true.
Governing of the turbine would have to be adjusted for the relatively low inertia of the rotor.
A different sort of clutch arrangement would be needed instead of the centrifugal clutch currently fitted.
Anybody still want to bid on the project?