That's fair. My $.02:
What about a sort of revenge mechanic? Yes, it'd apply only to when taking/mitigating damage, but, so long as OT mutually exclusive choices (e.g. 10% mitigation and insignificant healing to co-tank vs. 20% mitigation on self) remain inferior to the personals they share CDs with, we're pretty well obliged to swap in and MT whenever there's damage to actively mitigate (and our mitigation sources ready are presently stronger than what our co-tank has available). Mitigating more = more counter-attack damage = damage balancing in a "tanking" way.
You can also apply buffs that last for a certain amount of damage to be taken, with a bit of server delay on their removal that doubles as a hidden buff. For instance, imagine if Shelltron were to apply a 12% HP shield which causes you to block all incoming attacks so long as it remains. Even if you only have 1 Shield HP left, you still auto-block the whole effect. Well, if your initial mitigation is stronger, that shield is also going to take longer to break, which means more blocking-based mitigation, which means... You get the idea. Likewise, with your Whirling Step effect above, if you had a temporary evasion/expertise buff that could be used to maximize either damage or mitigation, but rarely both in that the first strike it mitigates will consume most or all of the buff, stronger mitigation allows you to better double up the effect.
Edit: That being said, I'd honestly rather get rid of Tenacity, Direct Hit, and Piety, and have each role gain additional tailored effects from Determination, Critical Hit, and Speed... (Tanks, for instance, would recharge their means of mitigation more quickly via Speed, their effects would be dynamically increased via Determination (effectively, consuming a hidden resource in order to ensure that X mitigation type is "just enough" to reach some breakpoint, usually survival or debuff prevention), and Critical Hit would unlock bonus effects (so we don't rely on it for last-ditch RNG mitigation so much as it generates interesting counter-offenses). So, instead of 1 weird stat that's supposed to be more role-purposed, but is either obligatory or ignored, you have three different fitting stats to choose between.