Going through the transformer details, it may just be damaging the transistors.
Each half of the primary is apparently 15 turns, which will have near 12V applied.
The secondary is 20 turns end to end, so a higher voltage than the primary; One end is limited to the base conduction voltage of the transistors, so the other end is driven strongly negative, likely putting more than -12V on the other base.
The datasheet Vbe rating of a 3055 is only -7V.
I'd be tempted to add eg. 2.2 Ohms in series with each base, plus another 2.2 Ohms in series with a high speed rec between base and emitter so that conducts when the base goes negative.
That should protect from both excess base current and excess negative voltage.
You could even try it with one ohm resistors, that should still be within safe limits.