Boost converter MOSFET shorting
You have two coupled coils which you describe as &quot;look[ing] like a coil around the original inductor&quot;. You need to understand that this is a transformer, and all the rules governing transformer behavior apply to it. As it &quot;looks like a coil around the original inductor&quot;, it probably has a coupling ratio very close to 1. You describe the turns ratio as being 1:6, with the coil with fewer turns feeding the gate of your MOSFET.
You measured 251.7V across the capacitor. At some point the voltage across the primary was 251.7+0.7-8.0 = 244.4V. The voltage across the secondary was about 1/6 of that or 40V. The voltage at the gate of your MOSFET, at that moment was about 40+8=48V. That exceeded the allowable gate voltage of 40V (transient). Hence your MOSFET died.