Yeah, action points (or hero points) seem to be the consensus choice. Now in D&D4 action points just get you an extra action; this action can be healing, rerolling an attack, or whatever, but that depends a lot on class, race, paragon path and so forth. So it simulates some effects of Righteous Burning Fury, but not all of them; in particular, it doesn't change the war-of-attrition dynamic that you rightly emphasize.