So I have an idea for this that probably won't be that popular, but will solve at least one half of the problem: have dps stances for tanks increase their damage taken by 20% or so. That way, either the healer can keep more to healing the tank who is now taking far more damage, or the tank can keep up tank stance while the healer's dealing damage.

With DRK, it'd be tricky, but probably tie in a bigger increase to damage taken when Blood Weapon is up.