I don't think a complete lockout where he just "ults" the nearest person would work well, but you may be able to add extra effects (negative/Positive) to abilities when at full rage. For example you may have an ability that gives you an empowered auto, but at max rage it turns into multiple empowered autos but taunts Warwick onto his target until all autos are spent.
Although one other thing that would could be kind of cool is instead of rage give him bloodlust. Bloodlust would go up when he was near enemy units with low health. and would go up faster when attacking enemies with low health. Blood lust would give him bonuses and penalties as it went up. The only way to lower bloodlust is to leave combat.