The overall scope of variation in a B20K is identical to that of a W20K. The 0%, 50%, and 100% positions will be identical, and anything in between will be equally attainable with either pot taper, just in slightly different positions. If you’re not getting an appreciable change in tone from fully CCW to fully CW, the pot taper is 100% not the issue. If the problem is just that the difference between 12:00 and 1:00 on the knob isn’t as noticeable as you’d like, then it would be an issue of the taper.
Plenty of TS clones use a B taper and it’s totally fine— just makes for some slightly different knob positions for specific settings, but any setting that would normally be possible is still achievable.
You said that you checked your resistor values— check that everything is soldered properly, and check your capacitor values.