AM modulator's negative peak saturation issue
Saturation to negative means very low resistance of the MOSFET at positive input, obviously short caused by body diode. You can see current of the feedback resistor is not equal to drain-source current in your simulation. The same thing may be happening in your board.
I'm not sure of how to make bidirecrional variable resistor with MOSFET, but hope this helpful to you; https://www.edn.com/a-guide-to-using-fets-for-voltage-controlled-circuits-part-1/