I had an idea that i feel need to be investigated....so here it goes...
imagine a transformer having two primary winding and one secondary winding... the secondary being in the middle of the two primaries what decouples the two primary a little
the two primary will have oposite fields so they will be pulsed at the same time for start than they must be sequencialy turned of
the idea is that if they are pulsed at same time their magnetic fields will cancel but when they are sequence turned off one first and next the other it will create an ac voltage across the secondary, one half cycle per primary turned off
as the coils are oposite in magnetic field they should saturate with current very fast, allowing both to have their time of collapse..
the main idea is that we can possibly charge both coils at same time and as we sequence turn them off they will have a sharp flux change
to achieve this we need a power supply and two independent switches
the timing circuit could be made with 555 timers and some inventive spirit
the two pulses must start in sync than one will terminate, and the other remain a little and than it terminate too and than there is a time with both off for the collapse to end for start over again..
so maybe one timer being the master clock and the second being a monostable