Don't try to make this problem more difficult than it is.  The answer to your basic question is yes.  It is possible, even recommended, to directly select the gear reducer based on motor input power.  The gear reducer selection should be made on the basis of the motor power and the reduced output speed.  The maximum torque will always be less than the power the motor can deliver at the reduced output speed, otherwise the motor will over load.  If the existing process conditions do not overload a 2.2 kW motor with an output speed or 36 rpm (0.6 1/s), then the gear reducer should be sized for a 2.2 kW motor.  2.2 kW = 2,000 W = 2,000 Nm/s.  Torque = power / speed = 2,000 Nm / (0.6 /s) = 3,333 Nm.