On a 3 rotor in economy cruise, would it be possible to completely shut off the center rotor fuel injectors and just pump air? I am sure friction losses would not be much, and fuel savings could be high. Many cars do this now by shutting off the valves or some other method. Would the lack of a power pulse unbalance the engine?

Definitely.  Don’t go there.  The three rotors fire at equal intervals so I expect it may not make any difference which of the three you shut down.  Having run briefly with one rotor not firing (don’t recall which one); it’s pretty rough.

Al