Sure you have got distortion on the sim .You will get it in real life .Try making the input volts 10 volts to reduce diode effects .If this helps then place a  DC voltage source in series with your AC generator.Experiment with a start value of say half a volt .Most AM detectors are prebiased to remove some diode nonlinearity .Then reduce the RC time constant accepting more ripple .Now you can postfilter to get the ripple down to an acceptable level .Often a RC section is adequate .I have used fullwave bridge   to   get  low    2F ripple that is easier to postfilter .I have benched a germanium prebiased fullwave bridge that performs well .If you have spice models for these then you could try .  Now things can get worse when modulation % is increased like 90% .When you do this on the sim you will have to do more optimisation.