I do not see the purpose of the rectifiers between the two transformers. I only pushes a strong DC components through them, and their cores may saturate.
Overshoot with ringing is usually due to a reduced circuit transient damping. If a snubber across the first transformer did not help, then try to connect a variable potentiometer across the second transformer primary, or remove the two diodes and replace them with the variable resistor.
Long connections can also contribute, as well as the parameters of the two rectifiers between the two transformers. Still unknown their purpose?
I am missing a capacitor across the Vcc for the MOSFET switch. Is there a magnetic coupling between the two transformers? How did you measure the output voltage? Your oscilloscope probe can pick up transients showing up as ringing.