Slayer Exciter : Aiming for Larger Arcs
Slayer exciter circuits are by design very inefficient. It is nothing more then a simple resonant circuit operating in a lossy manner. To get bigger sparks you need something more like a Tesla coil operating as a class D amplifier. Adding more turns will add resistance and reduce the resonant Q factor of the circuit, eventually giving you even less voltage gains for exponentially increasing amounts of power.

I would suggest you spend some time reading up on Tesla coils. Basically you are switching FETs or IGBTs on and off, not partially driving them in a class A style like the slayer exciter does.

A small half bridge Tesla coil can get you 1-2 ft arks and cost under $50 to build if you keep it simple. That being said, if you are not aware of the dangers of working with high voltages, building a Tesla coil is a good way to toast yourself.