When accelerating hard from 35 MPH to 60 MPH the engine oscillates and brings steering wheel and gearshift vibration?

There is a strange vibration. 5 speed transmission in 3rd gear accelerating hard from 35 MPH to 60 MPH, engine oscillates and brings steering wheel and gearshift vibration to extreme. Can be felt in other gears. I have balanced tires, cut rotors, replaced front center motor mount, and reduced vibration by 50%. It seems the root cause of vibration still exists. On rack with brakes applied and torque applied to drive line engine seems to set up an oscillation when brakes and engine speed simulate road condition noted above. Found right upper motor mount body securing bolt shifted to left side of car (tight), when loosened motor shifted to right side of car and some of the vibration was eliminated. It does not appear that axle shafts are bent, or Michelin tires have hidden defects. Note: rack test was with and without tires still vibration. Has anyone seen this problem before? Please help. Thanks!