Wait a minute, maybe I don't understand something here.
The wire size is dictated by the size of the breaker and should be big enough to handle what the motor needs. On start up the motor will draw more amps
than stated on the motor and the breaker is forgiving for a second. Motors are stupid they just take what they need, changing wire size is just asking for touble or did I miss something.
Yes, normally motors want a 'stiff' (low impedance source resistance) to start up properly while under load like this pump.
The temporary high resistance switched in by an NTC thermistor or a relay/ resistor may be enough to stop the noise for one second without unduly shortening the life of the motor.
I guess another way would be to use a damped spring coupling between the motor output and the pump input shaft, with the coupling providing temporarily more acceleration difference between the motor shaft and pump shaft which then dwindles to nothing.
Try the easiest first to localize the problem and than pick the optimum long term fix.
This issue is in addition to the current vs time needs of the motor, going from high current to low within a few seconds, and the breaker current vs trip time taking perhaps a minute or more to trip at 2x rated current and maybe 0.16 sec to trip at 6x overload.
This is another messy interaction but can be solved graphically. Matching a breaker trip curve to a pump motor current vs time curve may not be that easy, but the two curves should track other with a slight offset at all places on the curves.
If the OP really only needs 1/2 hp, feed the 1 hp motor 0.707 x 220 v = ~156V [{156^2}/{220^2}= 0.5 ] and adjust to get the noise reduction and power necessary. Now we're were back to a VFD or PWM modulator or a step-down transformer.