[sdiy] Center Detent dead zone on an "attenuverter"?

[Chris McDowell]

Howdy list, 

I have a very simple 4 channel mixer that has "attenuverters" (gain from -1 to +1) on each input. As it stands, the "off" position is super narrow and not exactly in the vertical position of the pot. Both of those were expected, and it's fine for anything that doesn't need to be silenced. Using a pot with a center detent leaves tiny bit of gain one way or the other, since the pot and summer resistors aren't exact. So, I wonder, is there a reasonable method of adding a dead zone to the center of an attenuverter like this, without trimmers? 

I can link to a pic if needed, but the circuit is straightforward and many of you are likely familiar: Input goes through a 100k to the wiper of a pot, two inverting amplifiers are in series, with the one leg of the pot going to the first inverting amp, and the other leg going to the second inverting amp. 

Initially I thought to myself "yeah easy, back to back diodes like on a pitch bend wheel" but about 1 second later realized that it's not at all the same situation. Back to back diodes on the output would have the desired effect when the pot was centered, but would not with any gain applied. 

Any pointers appreciated! Thanks,
Chris