If it only starts to work at 12 o'clock with linear pots then with log it will be worse. With linear, 1/2 rotation is 50% of the resistance, with (most commercial) log pots this equates to 10% of the resistance.
Try wiring up a log pot backwards to simulate a C taper pot. If that works OK either leave it like with reverse-operation controls, or order some C taper pots.
The volume shift is a characteristic of the design. Amongst other things the NFB changes due to the varying cathode resistance - more NFB as the depth increases, so lower effective gain.