That will work only with a different type motor.

Usually any single phase speed control REALLY looses torque.

You are better adding auxiliary pulleys if low cost is the main concern.

The pulleys will increase torque, and give you the speed control, at low cost.

I did this for a specialized sewing machine my wife purchased. It was designed for commercial super speed.

Now the variable speed is half, and the torque is double.

When multiple pulleys are used, REALLY small (narrow) belts can be used.

Sears used to sell a drill press that only needed 1/8" wide belts.