Adjusting wiper or adding a resistor???

[tinycat]

Is there anything I can do to just change how far a wiper rotates?  I really love what I'm getting with this knock off kids keyboard and a 1M pot, but if I push it too far it cuts out on me.  I'm digging how drone like it's getting, but it just barely gets passed it's normal higher range and stops working.  I connected it to ground and that helped a bit, but there is still just an ever so slight bit of room left that it just can't get past.  Would putting the old resistor somewhere in the line fix this problem?

[SamVsSound]

Is the keyboard cutting out as the pot adds more resistance or as the resistance gets lower? If the sound cuts out when the resistance gets to low adding a resistor can buffer this so that the resistance never drops below a certain value. If the keyboard dies when you add too much resistance you may have to swap out for a smaller pot, you could use a combination of a resistor and a smaller pot to get the resistance right up to the point where it starts droning without going beyond.