The bottom line is that the Herzog is easier an easy way to adapt a small amp as a distortion pedal, or a really bad way to build a tube-based distortion pedal. The benefit comes if you already have something like a Champ to use in this way.
Could you possibly drive your speaker off the cathode of the 6v6?
This is a good idea, as the cathode output would be lower than the plate output. But the cathode bypass cap will shunt any a.c. to ground, so you'd want to eliminate that.
Spit-balling ideasTaking the output from the cathode would lower the output signal to be about the same as the 6V6 input signal. This is still bigger than the voltage present at the speaker terminals. A typical Champ has 18-19v across the cathode resistor, and an output tube runs out of clean power when its grid is driven close to 0v momentarily. That implies an 18-19v input signal to the 6V6 and ~18-19v of peak a.c. output at the cathode.
19v peak = 19v * 0.7071 = 13.4v RMS at the cathode. Assuming the Herzog makes about 3w with its OT and 10Ω load resistor, then the voltage across the resistor is √(3w * 10Ω) = ~5.5v RMS.
You could split the cathode resistance into 2 resistors, one connected to ground about 1/3 the original cathode resistance and the other from this resistor to the 6V6 cathode of 2/3 the original resistance. Take the output from that tap point to knock the cathode output signal down to about the same level as the Herzog output (it will really be 13.4 / 3 = ~4.5v RMS).
You still have the same problem of having an output transformer as the plate load for the 6V6, or a suitable plate choke in its place (this wouldn't be a power supply choke). A Champ OT is $30, so I don't think you'll save much on cost or weight by using a plate choke for the 6V6.
And we're still left with the problem of having a
power tube not called upon to deliver any power output. You could run the 6V6 at low supply voltage (like 50-75v) which would drop down the power output, the bias voltage, the input signal level to drive it to distortion and the plate/cathode output voltages. But if we go through all that to make a power tube not deliver power, it seems like we should be able to use a smaller tube instead.
It would seem if you want a "tube distortion pedal" the Herzog makes sense if you're also going to have a speaker output to use it as a low-watt practice amp, or if you already have a Champ or a Valve Jr or the like for conversion. If you are opposed to having the output transformer, maybe for budget or space/weight reasons, there are plenty of easier, cheaper and lighter ways to create distortion.
At least, this is what I think I see when thinking through everything.