Majofa, I like your tiers idea, and here is an example of how I think it should work. Divide elements into either 3 groups of 4 or 4 groups of 3. For instance:
1. Darkness / Death / Water / Fire
2. Air / Aether / Life / Entropy
3. Time / Gravity / Earth / Light
A team's element can come from any group, then the personal element must come from a different one. How you split the elements is up to you.
Also, if you wanted to do that "ban" thing with elements, simply make it so your battle element can't be from the group your team's element is from. Or personal element but that would be more complicated, I think, although probably more diverse. You couldn't do both bans off team and personal elements unless you had four or more elemental groups.