if your metric is revolutionary new physics discovered per dollar.
Why do you think that anything revolutionary or even new can be discovered that way?
Lightning has recently been found to generate positrons via gamma rays. This is very recent science and definitely underexplored and not yet solved via theory.
http://science.nasa.gov/science-news/science-at-nasa/2011/11jan_antimatter/
http://www.agu.org/pubs/crossref/2011/2011EO220001.shtml
(more research on this appreciated by anyone that's up for it)
A Tesla Coil this large looks a lot like a lightning generator, an opportunity to explore the space where electrical arcs become lightning.
Lightning had also been hypothesized to produce x-rays for a long time, with evidence of x-rays in lightning only confirmed in 2001. The creation of x-rays by lightning bolts is also not completely explained by theory.
Basically, lightning is extremely poorly understood for such a basic natural phenoma and there is ample room for exploration, possibly leading to economical ways of generating antimatter.
Hmm, I think you are shooting a bit too far.
A quick estimate says that to generate ~1MeV gamma rays required for the electron-positron pair production you need at least 1MV potential difference between the towers, or >10MV/m electric field, given that the distance between them is < 100m. The dielectric breakdown strength of air is about 3MV/m, so you are not even at 30% of the minimum required energy, not accounting for any losses.
Maybe they can somehow build up enough voltage by isolating the electrodes with paraffin, Teflon or even glass, then extremely quickly open a gap for the discharge to take place, but this is quite hard to do and their current design implies nothing like that.
According to the comments, they are much more likely to play with the Schumann resonances, which is a rather more modest objective.
"If the government is not willing to fund the building of two 10-story tall Tesla Coils, then why the hell do I even pay taxes?"
This seems like by far the best investment of $300,000 out there, if your metric is revolutionary new physics discovered per dollar. I pointed the founder at Thiel's Breakout Labs, which is probably more suited to this kind of thing than Kickstarter. But there is still a very non-negligible chance that the Kickstarter Grant will come to fruition.