The signal looks like it is being chopped. Is this because of how you implemented the VCA (using a 4066 as an attenuator by pwm of the switching frequency) ?
The switching frequency should be high enough not to be audible (and visible given the time scale of the plot I expect, but I’m not sure), or else you get an effect similar to a ring modulator.
Do you filter out the VCA chopping frequency from the output signal or don’t you have any dogs in your neighbourhood ?