Increasing diode clipping influence
IC1 is a voltage amplifier.  It's job (so it thinks) is to put a voltage on its output that is a bigger version of the voltage on its inputs.  R14 is a high enough resistance that IC1 can push it around at will -- basically, you've hooked a Mac truck up to a wet noodle, and you're wondering why the wet noodle isn't affecting the truck's behavior.

Try moving the common terminal of S3 to the other side of R9.  If you like what happens, you may also wish to experiment with reducing the resistance of R14.