Bart, For this reason I used 0.1uF capacitors on the bridge and ground, to help prevent issues if my primary gets hit. Followed this diagram:
http://stevehv.4hv.org/DR_plexi/general%20wiring%20scheme.pdf
I also used a bead on the GDT as suggested in the diagram, which did clean up scope waveforms. Maybe steve can shed some light here, but if I'm not mistaken, it allows a streamer to hit your primary without things exploding. I beleive this was how steve made his coils where you can see just a primary, and streamers hit the thing without it caring at all.