This is really cool! Very original idea for controls, a clever way around the one button limitation. It's fun how you almost have to get into a rhythm. I also love the detail in having three difficulty modes, which definitely distinctly feel progressively harder.
To improve, I would take a look at collision boxes. I got stuck between a corner and a ditch obstacle at one point (along the upper right path) . In addition, on the hardest difficulty with the quickest speed, I went through and got stuck in the tree walls.
However this is a very clever game! Well done.