Sure there may be some multiple variants of SRS circuit tuning, for the circuit in Atlas book, in staring mode the voltage on the primary winding is just 40V so apparent 'resonance' is really weak. BUT if you look at vector diagram you'll see the voltage at choke winding and at capacitor is in-phase, which should not be a case for a series resonant LC tank. So may be a better model for the circuit will be a step-up auto-transformer (fed by a capacitor current) made from primary and secondary windings unbalance?

That is indeed how i imagine it. There is (unbalance L) + C series circuit, which does not have to be in resonance but to pass the desired current for filament heating. Then the rest of the winding steps up the voltage

The phase diagram may vary somewhat between manufacturers - Eltam use a different capacitor value than UK manufacturers. Also, i have seen moderate++ success with Eltam ballasts starting 36W T8's, something which is not supposed to work according to descriptions by UK users

Would definitely like to dig up mine and provide here whats possible

also should be noted SRS ballasts for 18W SOX lamps where quite common (as they officially require about 300V to strike, so an SRS ballast was seen as a good way to generate that in a compact low-loss-ish ignitor-less setup that also has the added benefit of inherent PFC correction)

https://www.lighting-gallery.net/gallery/displayimage.php?pos=-116224

(I was always a bit annoyed how they tied the coils together into a single terminal like that, so you cant use it with a regular 2ft tube or 18W-24W PL-L or 28W 2D if you wanted to LOL)

I actually think in the absence of the need to preheat the filaments, there is not necessary to have two parallel 'long' windings to the electrically hot tube end. And attached is a simple inductance with a tap circuitry actually inside the choke you pictured. Electrically, it is equivalent to the SRS circuit with asymmetrical windings, but with less copper as you throw away paralleled parts of the windings.

BTW it seems that SRS and like circuits still inflict a fraction of its capacitor value parallel to the tube. Slightly dampened by winding resistance, and leak inductance, but still here. As we all know discharge lamps do not like pure capacitor ballast or large parallel capacitors, this probably leads to high current crest, shortened life and like ailments... May be one of the reasons SRS circuits lost their popularity (in addition to high copper costs).