Oh interesting... I've done a few discrete things myself but never with common-base.
What are the inductances -- measured? k? Phasing correct? The P:S ratio or k_L3L4 is particularly unbelievable, but other than that, it would probably work.
I think operation is an unregulated forward converter: primary turns on, same phase appears on L4 (so the dot drops below GND), D10 conducts, D9 conducts momentarily (T2's k will almost certainly be lower than given, for which D9 provides a path until the leakage inductance charges up), and C4 gets charged to some ratio of primary voltage. This is more like a transformer-coupled charge pump than a converter, since the voltage on C4 is obtained straight from C2, PSRR is nil (Vout proportional to Vin), and efficiency is worse and worse at low Vo (being especially dangerous during startup and fault conditions). The transformer ratios need to be slightly mismatched (T2 lower than T1) to deliver the excess emitter current required to maintain saturation; it latches on until inductances charge up enough to break conduction, at which point it turns off and positive feedback accelerates this; flyback is clamped by D7. (Evidently, T2 discharges through C3+R6, D8 blocking avalanche breakdown of Q1. C5+R5 also help, though being almost the same value as R3+R6 they're probably to snub T1.)
Maybe helpful as a comparison, an LED driver I built some time ago:
This uses a saturation commutated, self-driving switch function. The
Seven transistors act as a variable frequency oscillator and error amp, regulating output current (comparing to a Vbe). The oscillator has a one-shot sort of function, switching current into the 60t primary, which then turns on the power transistor, and load current through the feedback winding maintains it on, at a forced hFE(sat) = 15t/3t = 5. This is a proper buck regulator, so the catch diode and inductor (the #26 powdered iron didn't work out, I later changed that to a ferrite core -- never updated the schematic) filter the output into LEDs, and no output filter cap is needed because the ripple current only costs a bit of efficiency. And it runs at full brightness all the time, no adjustable range, so, no problem with discontinuous current flow or anything.
If you made some transformations on this circuit, I think it might end up looking similar to your example. First, this is a buck converter; it needs to be made an isolated forward converter instead. Make the choke into a primary, ground the one end, and add a catch diode for flyback (reset flux). Given the single supply, this should be a CT winding with the far end going to a diode to +160V. Also, the transistor is high side, just swap that around, so now the transformer CT is +160V and transistor is at GND side. Move the feedback winding to the secondary side, adjusting the ratio accordingly: if the power transformer is say 12:1 (for a ~12V output), and an hFE(sat) = 5 is desired, then a 5:12 ratio is needed for the secondary feedback winding to the base drive winding.
The DIAC serves to kick it on; apparently it's free-running, probably the ringdown (after the catch diode turns off) is poorly damped and it turns on for another go pretty consistently. The DIAC is only needed to kick it into action at all. In this circuit, of course the regulator / oscillator serves the same function, and then some (because the buck topology permits regulation).
The above example, could also be considered a half-wave Royer converter: the transistor turns on until magnetizing current in the drive transformer rises faster than load current, thus reducing hFE(sat) and eventually turning it off. In particular, a small transformer is chosen (indicated turns on a 0.37" #43 ferrite toroid), which saturates, i.e. the magnetizing current increases suddenly and massively after sufficient on-time (here, about 10us). Saturation costs a bit more core loss, but this is in the smaller drive transformer where it's okay, meanwhile the sharpness greatly improves switching efficiency. (A Royer can also be done with a saturating power transformer, but this costs both core loss (the power transformer itself is running up to saturation) and switching loss (basically the saturation current forcibly yanks the oscillator out of saturation, forcing commutation).)
This might be a relevant mechanism in your case as well; depends on the core size in the two transformers.
Oh, finally, the D5 into C3 thing, is commonly seen in CFL converters as well: these use a full-wave (half bridge) current-feedback topology, of a very similar sort but the resonant load provides commutation, no need for saturable transformer hijinx; but it doesn't start up, so there's an RC charging network into a DIAC, and a clamp diode that simply keeps it discharged while the bridge is switching. So, as long as Q1 is saturating from time to time, D5 keeps C3 discharged, keeping Q2 from turning on.
Tim