Brain Teaser: Circuit Design

I recently saw this brain teaser apparently given to senior students by their professor for extra credit. (They had to explain and demonstrate a working circuit)

You are given the following BOM:
1) Two resistors (any value of your choice)
2) Two general purpose bipolar transistors (2 x PNP; or 2 x NPN; or 1 X NPN and 1 X PNP of your choice)
3) One low frequency crystal between 30kHz and 50kHz (suggested using 32.768kHz which is a common obtainable watch type crystal)*
4) One fixed value capacitor of your choice.

Design Specs:
1) Design a crystal controlled oscillator that operates at or within ±5Hz of the crystal frequency.
2) Output should be a sawtooth at the crystal frequency with a linear ramp characteristic.
3) Output impedance is not important as long as it can be measured with a standard scope and 10MΩ scope probe.
4) The amplitude of the sawtooth must be between 1.5-3.0 Vpp.
5) Circuit must not consume more than 2mA from a 12V supply and (not be frequency sensitive to supply variations of ±1V).

I thought it would be interesting to see what designs members here can come up with.

* Any old broken electronic watch should have an 32.768 kHz crystal inside. https://en.wikipedia.org/wiki/File:Armbanduhr_Rueckseite.jpg
Another crystal that is quite common is a 38.0 kHz used in simple FM stereo transmitters for generation of the 19 kHz pilot signal.

Show and explain your design with any simulation results or actual measured results on a scope so other members may duplicate and learn from it.

I am trying to upload my design circuit but the network is bad. I will keep trying.

There was also a second part to the design problem for those interested:
Bonus credits will be awarded if your circuit design draws no more than 1mA from a 12V supply and still meets all the other design specifications.