Mods:

You coud get a 5 meg pot, one side to positive, one side to ground and the middle lug to the input of one of the inverter inputs to get assymetrical distortion.

You could increase the 100 ohm resistor on the "Current schematic" to reduce the voltage to the CMOS chip. This should give you more compression and distortion. It does improve battery life.

Increase the value of resistors going across each inverter for more distortion, decrease for less. You can reduce the inbetween inverter resistors for more distortion.

Reduce the value of the 0.1uF caps for less bass. The capacitors across the inverters cut high frequencies, increase for less treble. You can go as high as 500pF if you like it mellow.

Afterthought: The original circuit is way too bright-sounding, the 500pF high frequency-taming caps are a good idea. The circuit does cut low frequencies, which is normal for a distortion circuit, but not to everyones taste.

Tone Knobs:I don't have a tone control on this because I wanted it to be very simple. I tweaked the capacitors to get the tone I like (bright) and left it at that. You can easily add a passive Big Muff Pi contol, or the Marshall Guv'nor  to the output, it cuts volume, but the Hot Harmonics is plenty loud.

According to Jack Orman of AMZ, the CMOS output is high impedance and would need a high impedance buffer (eg. another JFET buffer set for low gain - no 10uF cap) before being connected to a passive Big Muff Pi contol. You could copy the EH Hot Tubes tone control, of course. So the volume control will load the output a lot, reducing volume and possibly frequency response. This may or my not be a good thing.

The other way would be to use the 3 unused stages to build a duplicate distortion device with 600pF caps instead of 22pF and use a pot to pan from one to the other.

If you want a tone control I suggest you add an FX in/out loop (adding 2 jack sockets) after the volume control and put a graphic EQ pedal in the loop. The bypass switch will also bypass the graphic EQ when you switch the pedal off. You can pick up a used 6-band EQ pedal cheaply. Or put a passive tone control in a separate box. The Marshall Guv'nor has a similar loop (probably meant for a digital echo really) using a stereo socket. A stereo socket would require a Y-shaped cable.

The point is that you have your distortion coming from one box, and the tone control in a separate box. The tone control can be a a Graphic or Parametric EQ pedal, or a passive tone control in a dedicated box. Or no tone control. I'm never very happy with the one knob tone control, so I think the Graphic EQ is a versatile solution.

You can have an FX in/out loop after the FET transistor stage to add a volume booster or another Graphic EQ. You can then experiment without having to resolder anything.

You can add an FX in/out loop to any pedal, of course, and switch a chain of pedals in and out with one stomp switch.

I'll do a schematic for the FX in/out loop eventually.