I very much like the oil submerged spark gaps too, but the problem is that the oil needs to be in constant motion otherwise the sparks will burn the oil and cause carbon channels to form. This means that you'll have to build a relatively complicated contraption such as you'll find in Tesla's many patents.
The charging coil is a very simple way to get excessively high voltages. When done correctly, it creates a resonant charging circuit with the capacitor, that resonates at the same frequency as your AC source. I didn't (consciously) use it, but in earlier circuits I used a ballast to limit the current. Inadvertently the ballast I used formed a resonant circuit with my primary capacitors at near 50 Hz. I was expecting 11KV but I killed my ceramic capacitors rated for 40 KV. That was an expensive lesson that I still regret as those ceramic caps were really fantastic in their performance.
If you'd like more details let me know and I'll do a separate post on that.