Presumably, that is a single-phase motor. Is it split phase, capacitor start, brushed? Brushed motors can be controlled easily as you suggest. The others can sometimes be controlled, but at a great loss of torque. Check out KB Drives.
My recommendation is to switch to a 3-phase motor and use a 1-phase powered VFD or switch to a DC motor and use a DC controller. The DC controller will be a little cheaper (about $100 on eBay), but the motor is more expensive. I have done it both ways. The DC option may give a little more constant speed, but the difference is slight.
John