This is an excellent post and I love the interactive demos.
> gradient descent ... ball rolling down a hill
Gradient descent is similar to a ball with no mass falling down a hill. Other methods (heavy-ball and Nesterov acceleration) are similar to a heavier ball rolling down a hill. I've written a post [0] on this with a visualization.
Given a quadratic model (most examples in post) there are some strong theory on convergence rates. Nesterov acceleration has at least linear convergence (which really means exponential). More detail can be found in Noecdal and Wright.
(I'm currently in Steve Wrights Nonlinear Optimization I)