You should post the exact specs for the fan you have, but GaGrown is right the motor needs a minimal amount of power to make the initial turnover happen. Your ultimate solution would be a variable-frequency drive.

YouTube - TEMCo How To: AC 120v Single Phase to 230v Three Phase VFD

I have the same issue, but in a 12v scenario. I'm going to experiment with using a timer that would run at full power for a few seconds then switch off leaving the regulated power to run the motor.
scrumby Reviewed by scrumby on . CAN-FAN IS WORKING TOO GOOD!! Hi All, MERRY CHRISTMAS!! Well the temp in my tent never gets above 71, tent is downstairs where the temp in the house is lower (about 4-5 degrees) I keep the house at 70 when home and 64 at night and when away, my therms memory shows that the lowest temp so far was 61.4 and the highest temp was 78 (one day when the filter fan didn't kick on) but normally the temp is right around 70 give or take a degree! example right now the temp in the tent is 70.4 and outside the tent it's 65.8! I'm running Rating: 5