I like your idea for magic with the four bases. Personally I feel light should be categorized under energy, and life should be bumped up to take its place. Which would make water a combination of matter and life.
Earth and water are both tangible, and are therefore matter. Fire and water are both life giving and represent life Fire and wind provide energy Earth and wind both push with force as opposed to fire which envelops
Although, through this reasoning, you could make cases for water and force or energy, as well as make a case for life and wind. I guess you could potentially circumvent the issue by saying the way in which the elements are used in the world doesn't apply to those concepts, or that while they are affected, it is not enough to be considered a core part of that element.