Forgive me for trying to help, perhaps I miss-communicated. I was just pointing out that its a Fixed Low Pass at 720Hz, not High Pass as you said in the post previous to mine.
I think what I said makes a lot of sense, and the Geo article is in line with that as well, I'm just stating that I agree with RG's explanation thus far.
The clipping stage increases everything over 720Hz.
Between Op-Amps, everything over 720 is reduced (6dB/Octave).
The tone control has a gain of 1, and can either cut above 3.2kHz at the input, or cut in the Feedback loop (adding more highs to the output).
I never claimed that the tone control added the mid-hump on it's own. In fact, I believe its the combination of the Clipping Amp's Filtering and the Fixed Low-Pass between stages, but I haven't had time to calculate that. That's just my hunch. I don't believe you'll find a mid-hump without the Clipping amp.
On to your actual question:
The easiest way to see what the 1k Resistor does its to put a pot in there. My bet all along has been that its just setting the gain to 1, but I cannot be sure, because I don't recognize the 20K Pot between (+) and (-) inputs as any typical op-amp circuit. You seem capable of doing this. I can suggest Spice or 5Spice or LTSpice, a program where simulating would be very simple. I'd do it myself, but I haven't learned the ins and outs yet. It's coming in a week or two for the lab I'm teaching.
EDIT: Thinking a little more, I'd like to suggest that the 220 and .22uF is not a typical low pass filter in that, its not a simple voltage divider with upper leg R, lower leg C. I see it more as, a side path, or a dead end side street. (Getting figurative here i suppose) Vin to (+), has a side route to ground via the 220/.22uF. The 20k controls the amount dumped to ground, but doesn't affect the cut-off point. Likewise, Vout runs through the 1K, to the (-) and has a side route to ground through the 220/.22uF, amount controlled by the 20k. I believe this is because the main signal is not passing straight through the 20K resistor as it is in the 1k/.22uF low-pass prior to the tone control. To test this I would disconnect the 20K from the (+) input. If this is the case, I believe the Tone Pot would only INCREASE treble, because it can only cut the treble on the feedback leg, but not the input. Just a theory.
I can, however, offer an explanation for why the response goes flat when you short the 220ohm resistor. Recalculating what the cut-off would be, assuming a resistance of 1 for the shorted resistor, the cut-off frequency is now 723kHz!!!, well above the human range of hearing. The 220oHm resistor controls the cut-off, put a pot in there and you've got a way to control the cut-off frequency as well.
For the record, I'm not some newb throwing out suggestions out of my rear. I'm an experimental research physicist. I work with electronics everyday and on during any other week I would love to breadboard this, document it, and give a definitive answer. I just may do that for myself at some point, but I haven't as much as a free moment right now. My apologies that all I can offer is discussion.