BSR turntable switch makes loud pop

I am using a late '70s era BSR changer in nearly perfect condition. It uses a ceramic cartridge, and is connected via a Lehman Black Cube SE pre-amp. (Yes it's a yardsale item connected to a $700 pre-amp. I am doing this for nostalgia, as the turtable was my grandmother's and I used to play with it often as a child. I had to steal the pre-amp away from my Stanton because the BSR's ceramic cartridge seems to require the special 470 ohm impedance setting.)

My issue is that the turntable makes a very loud pop, of random intensity, when switching off. The randomness of the intensity seems to imply that the pop is caused by the arcing action of the microswitch as it disconnects the motor at a random point in the AC waveform. Hence, a disconnecting at the full 120 volt point means the switch opens with the full current of the motor arcing across. Disconnecting while crossing at 0 volts means the switch opens with the no current arcing across. Use of ferrite chokes on the incoming lines of the pre-amp eliminates the "spike" of the noise, but the dulled pop is still quite loud.

Could this issue be resolved by the use of a zero-switching solid state relay? Basically, I am thinking of re-wiring the unit so that the microswitch carries only a couple milliamps and the the relay would switch the motor off at the zero point every time. What do you think?

Here is the relay I'm talking about:
Digikey part# Z166-ND

(P.S. I am not concerned about the acoustical/ mechanical noises. I am well aware that it's a cheaper machine and makes a good bit of whirring and a loud clunk when it switches itself off.)