I would place a high PIV freewheeling diode across the transformer primary. I suspect that you may be seeing the result of the arc 'quenching' with the primary still energized. At that condition the transformer magnetizing inductance will come into play as the secondary current rapidly drops to zero. This presumably gives rise to the ringing or oscillatory effect you see on your scope traces.
With the diode across the primary you may need to add some current limiting resistance to the input charging side rather than just having the 20uH inductor.

I've tried freewheeling diodes across the primary of the transformer. BY448, UF4007, etc. They all suppress the oscillation about 50% but its still there and the diodes eventually fail too. I'll work with it some more.

 

try the inductor in series with the Scr,

I'll give this a try too.