If you change the line frequency, the speed will change correspondingly. That requires a relatively sophisticated circuit that uses a variable-frequency power oscillator. Using a triac alone to chop portions out of the AC wave will cause the unit to run at the same speed, but with reduced torque.
I have sometimes reduced speed on a turntable like yours by remachining the motor pulley to make it smaller. This has been useful when the set originally had a 50Hz pulley that needed to be reduced to 5/6 the original diameter to run on 60Hz.
Fred Longworth