I was originally thinking to put a SSWSMS (simple square wave shaper made simpler) on each octave's output, but that could potentially be a LOT of knobs, so reducing it down to one would be nice. If you made the two 1M resistors into two halves of a 2M pot, and brought the signal in through the wiper, as you turned the wiper, you'd get falling saw-triangle-rising saw. On the other hand, if you made the two resistors fixed and put a variable resistor between D1 and D2, you could get triangle at max resistance, square at min.
Then I had the thought that rising and falling sawtooth waves probably sound about the same, so it would be really handy if you could have a 1-knob control that went square-saw-triangle. I think you could do it with a center-tapped pot, but that's somewhat of an odd item, and it'd probably be easier to develop an active version at that point.
Now I'm thinking maybe you wouldn't need the SSWSMS on every octave...