Tesla did a lot of research trying to minimize the distributed capacitance but at one point he suddenly stops trying, without stating a reason and without a solution.
I think your thinking is still too much inside the box
.A coil has an inductance, a resistance and a capacitance.
The inductance is the coil's resistance to changes in current through the coil.
The resistance is the coil's resistance to current through the coil (obviously).
The capacitance is the charge needed to create a voltage difference across the coil (exactly like a capacitor, actually).
You can take a coil and let it resonate on its own inductance and capacitance, so without top-load.
I think that the coil's total capacitance is partly made up of this distributed capacitance and partly of the coil's geometry (viewing the coil simply as a conducting cylinder).
It has experimentally been shown that a coil's self-resonance frequency can be calculated solely using the length/diameter ratio and the wire length. That means that the coil's capacitance and inductance (or rather the product of these) are determined by those values alone.
That again, means that by increasing the coil's (distributed) capacitance you decrease its inductance.
I think that the spike you are looking for is the voltage spike created by breaking the current through an inductor. For that you will need a large inductance and capacitance is irrelevant. Just connect it to a 12V battery, wait for some current to flow, and disconnect. You will get your spike. I did this with the HV coil of a distribution transformer (about 4500 H, that is Henries, not mH!) and got some unpleasant shocks.

Does that help? (no, I'm not referring to those shocks
)
Ernst.
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