How can I get rid of this spike in my overvoltage protection circuit?
The most basic way to get rid of voltage spikes is to low pass filter them. Make C1/C2 (1uF) bigger and see what your results are.

The other way is to make M1 shut off faster of course. To pinch it off faster, you would have to lower R6 so that the voltage spike travelling down the line transfers its energy to the Gate of M1 faster. R6 is the path to do that. 

Something that makes me wary of the circuit is the position of L2. It's most likely being used as part of a low-pass filter to begin with, but in the event of a voltage spike, the position of M1 with the inductor causes a significant voltage spike on the left side of M1 as M1 is shutting off. This could exacerbate the problem you're seeing. To get around this, you may want to add a diode across L2 facing backwards to allow any inductive spikes you cause to bleed out through the diode. Look up voltage-snubbers for more info on this.