Tesla coil with voltage doubler?

Artlav

I want to power a small-ish tesla coil from a 8KV 500W transformer with a voltage doubler to raise that to 16KV.

Problem is - it works considerably worse (shorter sparks, LOUD gap) than with a 30KV 100W flyback, spark gap being the same, set at about 12KV.

One issue appears to be that once the spark gap closes the capacitors in the doubler discharge across it as well.
Another issue might be that the doubler's capacitors are essentially in parallel with the tank capacitor, thus interfering with the resonance.

So, wide question is - how to make a tesla coil work well with a voltage doubler?
More specific, is there a way to make a current limiter to prevent the doubler from discharging all at once across the spark gap? Resistors are out of the question, obviously.