Single phase capacitor start induction motor TRIAC speed control and centrifugal switch replacement
Induction motors are locked to the mains frequency by design. If the rotor speed moves outside the required speed range, then the motor becomes very lossy - ie it draws more current and gets very hot.
Phase control works well with series wound motors like in your power drill - these are not induction motors.
You can find cheap 3phase induction motors with variable speed drives that will work from single phase quite cheaply. It is an off-the-shelf solution that just works.
Or scavenge a motor from a washing machine (if the motor has brushes it is most likely a series wound type) and then you can control the speed via phase control.