Tested -- works ....        This wave shaper needs an input saw that goes from Vss to (ideally) Vdd. It works well with the 4069 VCO designed by René Schmitz. Any saw will work as long as the wave is centered halfway between the rails. It works as follows: The upper set of 2 linear mode gates provide an inverted and noninverted copy of the saw. The 3 logic gates at the bottom provide a sort of comparator that switches at halfway between the rails. The 4007 provides 2 P-MOSFETs that alternately select the inverted or noninverted saw signal depending on where the saw is in it's cycle. This causes the ramp to reverse directions every half cycle. Any imperfection in the saw will show up in the resulting output. The linear mode gate furthest to the right provides soft clipping that turns the triangle wave into something like a sine wave. It sounds like it has fewer harmonics than the triangle.
To use with FatMan sawtooth output:
Power all ICs: Vdd = 0 volts, Vss = -12 volts. All ground symbols on schematic will go to -12 volts and all +V symbols go to ground.