Hi Adam.
Your circuit looks a bit like a self oscillating compact fluorescent lamp half bridge inverter.
Some more circuits and explanations here:
http://www.pavouk.org/hw/lamp/en_index.html.Basically the bottom half makes +/- 166v DC as you have already determined.
The node you measure as -33VDC is actually swinging up and down (50kHz) between +166 and -166v, it spends slightly more time at -166v , hence the average voltage is ~ -33v.
So for the moment, assume D1,R8,C12 are just a short circuit, and assume R6 and R7, D3 are non existent, ditto D2,R12,C13 are shorted, R11,R10,D4 are open circuit.....
----first half cycle----
If the top of T1 swings up say 1v, current will flow into the base of Q1, and Q1 will turn on, in the process it will pull "-33" up to +166, and draw current through the middle winding of T1, this causes even more voltage at the top of T1, ensuring Q1 stays hard on. After about 10uS T1 saturates, and the voltage drops to zero, this forces Q1 off, and without any current through the middle winding, the top winding of T1 goes negative (turning off Q1 even more), at the same time the bottom winding goes positive (it's drawn wrong here, there should be a dot symbol that is anti-phase to the top winding).
---next half cycle---
So when the bottom winding is positive, Q2 turns on , and drags -33VDC to -165v, this time the current flowing through the middle winding pulls the bottom winding more positive turning Q2 on harder, after another 10us the flux collapses, Q2 turns off. and the cycle repeats.
--------------
So now you have a +/- 166v square wave at "-33VDC" , this voltage is then applied to the primary of T2 , and the load is connected to the primary
====================
So that's the important part, the rest of the components are "garnish"
(a)C10 is used to ensure no DC flows through T2 (else it would saturate),
(aa) additionally C10 can be used to make a resonant circuit with the inductance of T2, this will reduce switching losses of Q1 and Q2
(aaa) if driving a compact fluorescent, C10 can cause resonance when the lamp is cold , creating a very high voltage that causes lamp to strike.
D3, D4 are free wheeling diodes, they conduct should the voltage at t2 exceed +/-167v
C11 and R4 are a snubber, basically the leakage inductance and interwinding capacitance of T2 ring at several MHz, so to suck up this energy we use a snubber
D1 R8 C12 are used for waveshaping, to provide a fairly constant pulsating base drive to Q1, with a max positive voltage of say ~ +1v , and going -1v negative with low mains voltage to -3v with large mains voltage, so R8/R7 gets warm with high mains voltage, R7 is there to discharge C12 on the negative swings.
R6 and R10 are for startup, a small trickle folows through each, cause both transistors to partially conduct, and they have a tug o war, the winning transistor gets to work the first half cycle.
You can control the power output of the convertor by periodically shorting out the left winding of T1, crude, but effective.
Hope that helps , Bob.