There's no magic about CTS pots, or cloth-covered wire for that matter. What good pots give you, is better longevity, and in some cases, smoother operation.
You can certainly some shift the tonal range of the bass by changing the tone cap. Even when the tone control is wide open, it bleeds off some highs.
A larger value cap (i.e.: 0.1) will darken things up, and a smaller one (0.22) will steal less of the mids when you roll the tone knob back.
Another trick is to install an SPST switch in the wire between the tone cap and the volume control. When it's closed, the tone control works normally. When it's open, the tone control (including the pot) is out of the circuit, reducing the load on the pickup, and brightening the overall tone.
You can also use the switch for a preset tone shift- dial the tone control back to a given value for your darker sound, then use the switch to toggle between that sound, and wide open.