Is my iPad not accurate enough or is it the stylus? I made some capacitive styli with my brother, following this video on Cnet. 

I tried using it with the Wacom notebook app, and the handwriting is a teensy bit too large to work as well as a real live "dead tree" notebook.

At the moment, the app feels like a wide ruled notebook, and I'd love to be able to write as much as a college ruled notebook.

Is the problem the tip of the sponge on my styli, or is it the resolution of the iPad? 

What can I do to improve the accuracy, so that I can fit more handwritten text on the page?
This is a limitation of the iPad screen. No stylus will feel like a real pen. Future versions will likely have more sensitive screens. The best you can do is think of it as a giant index card and a fat marker. 

The Wacom software improves the situation a tiny bit by having the zoom mode when writing. You can find other software that allows more zoom, which would make the final product look like a normal page of text, but the act of writing will not be improved.