Simplifying H-brigde circuit
simulate this circuit &ndash; Schematic created using CircuitLab

This h-bridge cannot have shoot through because the upper transistors are switched off before the lower ones are turned on and vice-a-versa.
There will not be quite +12V across the motor because of the transistor Vbe drops so it will run a little slower.
Don't forget to add the back emf snubbing diodes.