AM modulation circuit modification
The emitter of Q1 is connected to ground which means if the collector has a negative voltage due to the V3 input voltage, the transistor is in reverse active mode.

You don't want that to happen as the reverse active mode has vastly different parameters than the forward active mode. Most manufacturers don't even specify parameters for this mode as they can't control them properly during manufacturing. Creating poor symetric transistors is simply not their goal.

You have to put the low frequency source V3 between the emitter and ground and connect the collector to V+, so the emitter is at a lower voltage than base and collector for any polarity of the low frequency source V3.