What is the best way to force yourself to master vi?

First of all, you may want to pick up Vim; it has a vastly superior feature set along with everything vi has.

That said, it takes discipline to learn. If you have a job and can't afford the productivity hit (without getting fired), I'd suggest taking on a weekend project for the sole purpose of learning the editor. Keep its documentation open as you work, and be disciplined enough not to chicken out. As you learn more, become efficient and start relying on muscle memory, it won't be as hard to stick with it.

I've been using Vim for so long that I don't even think about what keys to press to search or navigate or save. And my hands never leave the keyboard. To use Vim is one of the best choices I've made in my programming career.

The first thing I'd do is lay a piece of paper or a book over your arrow keys and your ins/home/end/pgup/down keys. Those aren't needed in Vi.

Next I'd get used to hitting ctrl+[ whenever you're told to hit escape. It's much faster and you won't need to take your hands off the keyboard.

Then I'd watch my screencasts:

http://www.youtube.com/watch?v=FcpQ7koECgk

http://www.youtube.com/watch?v=c6WCm6z5msk

http://www.youtube.com/watch?v=BPDoI7gflxM

http://www.youtube.com/watch?v=J1_CfIb-3X4

Then, just practice practice practice.

edit The reason for avoiding the arrow keys is that they slow you down. One of the largest benefits of Vim is the speed it allows you. The arrow keys also prevent you from really embracing the modal nature, which is very powerful when mastered.