Success, kinda

I switched to a larger capacity battery so I could more completely saturate the transformer coils. This has allowed me to more than double the air gap the electricity is able to bridge. The measurement device I've been using doesn't read past 35,000 Volts so I have no idea what voltage I've managed to attain.

This is a gap of about 1-1/2 inches.
With this level of voltage I now have a strong enough Electromagnetic field that I can light up a compact fluorescent bulb with the induced voltage alone. It lights up dimly which is where my main problem stems from. In order to use this powering of the bulb for presentation I need to have a completely dark area for it to be noticable. This may not be the most effective means of showing what I'm looking at.