I can say that the pot of the LPB-1 is a volume control, so at zero you have no sound.
The SHO could be better, because the pot is a gain control, and at zero it shouldn't give you any boost at all, I guess. At max it boosts a lot.
But I think the SHO is not super transparent, and the stock gain pot is "Crackle OK", it means that make some noise when you turn it.
Starting from the SHO you can set with a resistor a fixed gain setting instead to use a pot, and to add a master volume pot, using a resistor (maybe a trimpot) to the ground to set the minimum volume. (In case I'll try to help you).
Or, you can use a op-amp boost, that I found less noisy than transistor based schematic, and enough transparent.
I found casually a simple one:
I drawn (but still not tried it) a simple schematic of mine of a op-amp booster. If you want I can show it.
Or you can see the MXR MicroAmp. OpAmp based, clean enough, transparent enough. The gain pot works as you want, just the tape is not so linear.
I build pedals