How to increase the overall gain on this circuit

Well you can modify the linear pot to get an almost logarithmic response by adding a resistor from the CCW side to the wiper. Because of its simplicity this might be worth a try. Here's what the idea looks like: -

For the pedal circuit you need this might be ideal. It's not perfect of course but it reduces the risk of buying linear pots because these can be made "almost logarithmic by adding one resistor.

One thing to remember is that if the design calls for a 1M pot and you have a 1M resistor across wiper to CCW, the end to end pot value will change as the wiper advance towards CW. This would probably mean that you should use a 2M pot and 2M resistor.

Some experimentation is required and if you could post a circuit I'm sure better advise could be given. Pictures gleened from here

EDIT - picture of circuit attached with my best guess at log/lin: -

First of all, I'm going to assume your complete circuit looks like this:

[BTW, you should post your complete circuit if you expect to get any meaningful answers.]

Secondly, the unity voltage gain of the common collector refers to AC, not DC.

From the image above, you can see that the output voltage will be \$V_Z-V_{BE}\$.

And \$V_{BE}\$ will have some variation with the collector current, but not too much: \$V_{BE}\propto ln(I_C)\$.

On the other hand, \$I_B\$ is not negligible, it could be up to 20mA (for the transistor's minimum \$h_{FE}\$ of 50), and you don't really show how you are biasing your zener, so it could be that the base is sucking more than you are providing and the voltage across the zener will drop, and this drop will be directly reflected at the output voltage of this circuit.

By the way, from the 2SD1047 datasheet, \$V_{BE}\$ at 1A will be about 0.7V, so your output should be about 4.3V (not 5V), and like I said, will vary a bit with \$I_C\$. At 1A, it will dissipate quite a bit: \$1A(20V-4.3V)\approx 16W\$. The transistor should be able to thermally handle it though, since its thermal resistance is only 1.25°C/W.