Just found the full design equations for the 8/20 µs surge generator in [1]. The author was nice enough even to have all component values precalculated for you. Looks easy if you can find a suitable HV switch. I initially worried about core saturation, the surge is 100 to 1000 amps, but the L is just 10 µH, a practical value for winding an air-core coil by hand.
[1] Elementary and Ideal Equivalent Circuit Model of the 1,2/50 – 8/20 μs Combination Wave Generator, Carlo F. M. Carobbi https://ieeexplore.ieee.org/document/6714698 #electronics