How to boost (double voltage) a sawtooth generator
I'm going to suggest something completely different.

Have a close look at the LM3900 quad Norton amp chip.  This chip is similar to a LM324 in that it has 4 individual sections BUT: the op-amps are current-input instead of voltage-input.

Because the inputs are current-input, it's trivial to create a linear ramp by configuring one section as an integrator.  The difference in input currents sets the ramp rate and direction (increasing or decreasing).  

Note that the ramp is a true linear ramp - not exponential as would be obtained from a simple RC network.  Also note that it is trivial to have separate adjustments on the rise time and fall time.  That means that you can have a slow sweep up (or down) and a very fast return in the opposite direction if desired.

You will use two more sections as comparitors to set the upper and lower bounds on the sawtooth.  The final section is configured as a latch to control whether the ramp rising or falling.

The main reason for suggesting this chip instead of a classic voltage-input op-amp is that it is so trivial to build what you want - with a minimum of components.

Start by building just the integrator.  Control the ramp speed and direction by modifying the input current to the inputs.  

Post what you've done and we'll help guide you to the finish.

FWIW - one of the most successful building (architectural) lamp dimmer projects that I did many years ago was based on the LM3900.  I basically implemented a phase-locked loop that adjusted the ramp time to match the frequency of the incoming AC power.  This was essential because the system was powered by a generator-based power supply that had lousy frequency accuracy and really poor stability.  

The main part of my circuit was exactly as I have described above - all I did was add some sample-and-hold stuff to adjust the ramp current.