Please post a scope image of the output when the distortion is happening and visible. Q12 and Q13 are not in the signal path. They are there for output current limit protection.
Listen to the output from the preamp out J3 on a second amplifier and see if the noise is there.
When in clean the drive knob should not do anything. That strongly suggests that you have leakage from the drive channel. Have you checked the voltage on the gate of Q4? Try shorting out D9 to see if the problem goes away.