But again, what is the _problem_ that needs to be fixed?
The situation is that you are forced by circumstances to use an oversized motor for the job, and _something_ about this oversized motor is making things not work.
If they installed a 10 hp motor of the same speed as the intended 1 hp motor, then perhaps there is a way to 're-rate' the motor by operating it at lower voltage; possibly by even re-connecting the motor for a higher voltage than the actual system voltage. If I may: what is the supply voltage, and is the motor a 12-lead motor?
In any case, if you are stuck with the particular motor, a VFD very likely would solve the problem, not by virtue of being able to control the speed of the motor, but by being able to control the voltage and starting current of the motor. One mode that some VFDs use is to reduce the voltage being supplied to a motor in lightly loaded conditions, reducing magnetizing current and total losses. The VFD would eliminate the initial inrush current of the motor, as well as the locked rotor starting current, and then reduce the losses as the motor is powering the very low load.
-Jon