With a 100kB pot:
Gain_min = 1 + (1MΩ/(4.7KΩ + 100kΩ)) = 10.55 (20.5dB)
If you wanted to sub the gain pot, you'd want to scale the feedback resistor. Also, you'd want to consider the series resistor and cap to preserve the frequency response. You'd have to scale the series resistor regardless so you could maintain the Gain_min behavior anyway.
I just built one and like many other people, I didn’t like the B1M. The bulk of the gain comes in only in the last 10% of turning it up. I imagine the problem would be there with the B100k too. You might want to try using a C taper if you can get one, either 100k or 500k.