My ASCII- artwork isn't nice.
Wat I mean is, pause, high, pause, low, pause, high, pause, low,.....
This we have to make on both channels from the pic.
If transistor1 is high, transistor2 must be low and between switching (!) there must be a break/pause.
The transformer in the new schematic is a normal transformer and didn't work as a flybacktransformer.
This transformer need AC and the problem is, we don't have AC so we have to make it.
But AC have a smooth sinus wave and we don't have.
The Voltage will go from high within 0 usec to low......and thats not good.
Transformers don't like the squerpuls we put into the transformer.
But1 transformers act analogous, so inside the transformer the squerpuls will be reformed to a sinuswave.
But2 we have to given the transformer some time to do this and this is the break/pause between the high and low switching.