Limiting peak power consumption with energy bank
Supercaps seem to be the best option. But you have to give it time to charge, so its best if you add a mosfet/relay which will turn the hard drive on via a signal from the raspberry pi. Also remember to add a diode in series to prevent reverse current.
I would have suggested you other ways but seeing that it is a hard drive motor and any mishap could affect the data on it (else I would've suggested a soft starter or a ntc thermistor in series with it)
Its best to put up with what the hard drive wants.