Generating a constant-amplitude triangle wave from a square wave
One solution is to turn the circuit around.  Rather than generate a square wave and then try to convert it to a triangle wave, generate the triangle wave with an integrator and comparator.  As you vary the integrator time constant, the square and triangle outputs track and both amplitudes are constant.  The R and C for the integrator set the frequency, and adjusting the trip point for the comparator changes the symmetry of the square wave.  The comparator hysteresis sets the amplitude of the triangle wave.

A quick search for 'triangle generator circuit' found this:



(Image source: Bill Bowden)

For a given frequency, the slope of the ramp in a saw wave is 1/2 that of the slopes in a triangle wave.  If you want all three waveforms available simultaneously and have them track with a single adjustment, there is no simple circuit.