An OpAmp will not be able to directly control the state of a MOSFET.  The OpAmp will be too limited in output impedance, slew rate, and output voltage swing.  You are going to want a device that can switch quickly while driving the gate capacitance of a FET.  

There are different ways to control the on and off time of the FET.  PWM is the most used, but there is also constant on time and constant off time.  Constant on time and constant off time can be used in a hysteretic regulation approach, using a comparator to sense the output voltage relative to a reference.  Whatever control technique you try, you will need to bound the on or off time of the switch somehow to have any reasonable control of output voltage.

As to the overshoot you see when the load changes:  

Did you put resistance in series with the inductor and capacitor in the simulation?  Real parts have loss.  If you have no loss in the buck inductor and filter capacitor, filter Q will be very high.  High Q LC filters will ring to 2 times Vin on application of a step.   

Buck converter with op-amp, inductor issues when load changes
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