I would say that Richard Parker represents none of these religions directly. Instead, he represents the challenge of matter. By that I mean, it is all well and good to study or construct complex faiths to explain the world, but what happens when you've got a tiger in your boat? When you face an immediate threat that surpasses those frames, and that is not itself obviously good or evil?
Richard Parker is like Job's tests or the catalysts that bring some to enlightenment. He allows Pi to show and develop his character.
And this is, I would argue, the answer to your fine mind/body questions. Like a mystic in the desert, Pi is forced by Richard Parker and the ordeal to move past the strengths of the mind or body, and to find peace instead in the spirit.