Sounds like envelope ripple. People regularly describe bad envelope ripple as "distortion". In this case it is essentially a kind of tremolo, but at audio frequencies.
A few things to check on. First, make sure the 10uf cap to ground from the Attack switch is the stated value and properly connected to ground. Second, make sure that the transistor is properly oriented for each half of the rectifier circuit. losing half the rectification can lead to more audible ripple.