The trick to figuring out the circuit is to realize that you don't want to use the transistors as "current amplifiers" in the usual sense. What you want to do is use them as switches.
Start with the PNP. With a 12 volt supply and a fully charged pair of caps, let's say we can turn on Q3 so that the voltage across is very low - a few tenths of a volt. This is called being in saturation, and the rule of thumb is that saturation will reliably occur with current gains of 10 to 20, as Spehro has answered. Let's be conservative and assume a gain of 10.
Figuring about 2 volts drop across the SCR gate and Q3, that leaves 10 volts across R23, which suggests that 50 ohms would be about right to produce 200 mA through the gate. This in turn establishes 20 mA as a base current for Q3. (Gain of 10, remember?)
The same desire to operate in saturation applies to Q2, and hence the voltage drop across R36 will be on the order of 11 volts. That is, 12 volts minus 0.7 volts Vbe(Q3) and minus 0.2 volts Vce(Q2). 11 volts is close enough. So R36 should be about 11 volts/.02 A, or about 560 ohms.
Finally, since Q2 is operating with a gain of 10 and a collector current of 20 mA, base current should be 2 mA. R27 should be about 2k.
If all of this seems rather imprecise, it is. There is no need for high precision given the relatively large range of current gains associated with saturating a transistor. Using a conservative estimate of a gain of 10 allows for very rough calculations to do the job. And since there are no high voltages or currents involved, the possibility that rough numbers will produce non-optimal component values simply doesn't carry much of a penalty.
You'll also notice that this approach is better than trying to tailor current levels via transistor gain rather than resistor values. There is a very good reason for this. If you attempt to operate the transistors linearly, in principle you could do away with R36 and R23, which might seem like a good deal. It's not. Individual transistors will have quite a broad range of gains, so you would have to select your transistors to get proper operation. And then you'd have to deal with the fact that transistor gains will typically vary with temperature, so all your calculation and selection would not guarantee proper operation in varying environments.