Trust FvM. his solution is best !
Consider what happens when one side of the transformer is connected to ground via Q7 or Q8, see what the polaity of the OTHER winding does at the same time and how the diode across it conducts.
Incidentally, the driver circuit is VERY prone to leakage current, it effectively has four bipolar transistors in cascade, the slightest leakage in Q3/Q4 will be magnified many times by the overall gain. If Q3/Q4 were mounted on the same heatsink as Q7/Q8 there could be serious thermal runaway problems.
Brian.