I wrote a long response yesterday, as promised, and I don't know where it went. Must have clicked on the wrong thing.
But the short version here....
1) Less "gain". The circuit shown on the tagboard site uses a 1k/220nf ground leg in the clipping stage. That provides for a max gain of 500+, and a bass rolloff similar to a TS-9. Change that to 3k3/100nf and that will drop the max gain to 150-ish and lower the bass rolloff down to 480hz, for a "meatier" tone. That will make the Gain control less "twitchy" for you.
2) The schematic I have (provenance unknown) shows a 2+2 diode complement, not 2+1. A 2+2 combo will clip a litle less obviously and provide more output.
3) The 1k/150nf pair on the output of the clipping stage provides less treble cut than on a TS-9. There is also no feedback cap in the clipping stage which assists in treble cut in the TS-9 as gain is increased. Consider putting a 68pf cap in the feedback loop of the clipping stage.
Wish me luck, I'm hitting "post".