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Use a topswitch with series inductance to generate step up voltage.
The design of inductor values can be got from Power integration Inc. or fairchild .There is no isolation as the ground is common.What is the actual load currents handled at 24VDC?What are the loads being driven,,will the switching noise have relevance?
The pushpull complementary stages are balanced but have their difference in the Hfe of the devices which causes one of them to saturate and drive other into cutoff.The phase reversed secondary has a ratio 1:4 which gives 3VDC pulse at the base drive of the OFF device and switches it ON.The resonant secondary inductance with the 100nF and static capacitance of load provide the frequency of propagation in the base drive ..The Q2 saturates and this drives Q1 into cutoff owing to phase reversal windings....The process repeats to generate 2x12VDC square switching .The transition time is small and gives perfect square wave with no losses or overshoots in the in the peak to peak performance of output .
As such ,need for snubbers does not arise to damp out ringing ..However , the Bmax of the ferrites needs to be 3000..
For 50watt conversion the size needed is EE30 with N67 --87 cores .