Today I went to my local hardware store to fetch some new cells. I was surprised at the price of the them (3.5€ for 2 CR2032), but it was definitely worth it. As I'm writing this, a new coin cell is not only pushing the capacitor well over the 2.44V barrier of yesterday, it can manage 6V without any trouble! If I change the coin cells in the middle of the charging process, I might be able to achieve even 12V!

However, I realized I have another problem: at 6V, he circuit isn't powerful enough to explode just any LED. I hope that it will be able to handle at least the small red ones, while needing at least 9 or 12V for the big ones.