A compromise pleasing everyone might be attainable...
When infils are caught failing an attack, it says they are caught with a poisoned dagger. Why is this poison ignored everywhere?
Add a new status: poisoned. Poison prevents one's condition from improving (though it can worsen), and lasts for a full day on a partial assassination and two full days for a complete assassination attempt. Then, make healing overall easier, so that a wound in battle or by preaching has less odds of keeping one out of action for a week.